T ime Calculations
TIME
CALCULATIONS
T
P OR
PASS
www.mathletics.co.uk
This booklet shows how time calculations are used in everyday life.
Time has been measured by many civilisations in many different ways.
Some early methods used include:
Observing the cyclic repeating patterns of seasons and astronomical events.
Watching the movements of shadow from the sun.
The flow of sand in an hour glass.
Water level in containers designed to leak slowly.
The height of candles as they burned down.
The changing weight/fragrance of incense sticks as they burned.
Pendulums and weights to keep clock machinery moving.
Q
A limousine driver needs to pick up a movie star from the airport at 6:15 pm.
Before he leaves he needs to spend 25 minutes washing the limousine and then a further 10 minutes
changing into his uniform.
The drive from home into the airport takes 45 minutes.
What is the latest time the driver should start doing these things so he arrives at the airport on time?
Work through the book for a great way to do this
Time Calculations
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TOPIC
1
How does it work?
Time Calculations
Units of time
Time can be measured in many different units. They have been finely tuned over the ages to what we
have today, with ‘seconds’ as the base unit of measurement.
Other units of time we are most familiar with in increasing order are:
seconds
minutes
hours
days
weeks
months
years
decades
centuries
These units of time relate to each other like this:
• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 day = 24 hours
It is incorrect to say:
1 month = 4 weeks.
Only February is usually 4
weeks long (28 days). All the
others have 30 or 31 days.
• 1 week = 7 days
• 1 year =
12 months
=52 weeks
• 1 decade = 10 years
• 1 century = 100 years
It is important to be able to imagine the length of time associated with each of these units.
Circle the time measurements which best match how long it should take to complete these events
(i) Complete a 2000 piece jigsaw puzzle.
6 minutes
6 days
6 weeks
8 days
8 weeks
8 months
(ii) Build a house.
Thinking in reverse is also important for daily planning when there is work to be done in a given
time frame.
(iii) Which of these would usually take 2 hours to complete?
Mow the lawn
2
H 11
SERIES
TOPIC
Paint the house
Time Calculations
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Sweep the kitchen floor
How does it work?
Your Turn
Time Calculations
Units of time
1
Select the time measurement which best matches the given event to reveal the name of ancient
time-measuring devices that used the flow of water in/out to run.
(i)
Ironing a shirt
G
6 seconds
(ii) heating water in a microwave
C
6 hours
E
30 minutes Y
3 hours
L
2 years
D
6 minutes
30 seconds D
(iii) Growing tomatoes from seedlings
2 weeks
S
2 months
E
(iv) Watching a river change direction
through erosion
2 years
R
2 decades
T
2 centuries S
1 day
C
30 hours
L
30 minutes R
1 month
W
1 year
P
1 decade
A
(vii) Brushing your teeth
20 minutes
I
2 minutes
A
2 seconds
E
(viii) Lacing up a new pair of sneakers
30 minutes M
15 minutes E
5 minutes
Y
E
5 seconds
R
(v) Writing an email to a friend
(vi) Building a road bridge
(ix) Double clicking a mouse button
L
1 second
3 seconds
C
(i)
(iii)
(vi)
(iv)
(viii)
(ii)
(v)
(vii)
Give examples of activities you like do in which you need to plan to keep each of these lengths of
time free to be able to do them:
(i)
30 minutes
(ii) 2 hours
TS
...../...
../20.
...
* U NI
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OF T I
O F TI
* U NI
TS
ME
(iii) 1 day
ME
2
(ix)
3
How does it work?
Time Calculations
Changing between units of time
The chart below shows what we multiply/divide time measurements by to change into different units.
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# 24
# 60
Here are some further helpful charts for converting between longer periods of time:
' 52
'2
'7
Days and weeks
days
weeks
#7
' 26
fortnights
#2
# 26
# 52
' 12
months
Months and years
years
0.25 days means
every four years
we have a leap
year (an extra day
in February)
years
# 12
' 365.25
Days and years
days
' 10
years
# 365.25
' 10
decades
# 10
centuries
# 10
Use the conversion charts to change these lengths of time into the units given.
(i) 4 years into months
4 years = 4 # 12 months
' 12
months
= 48 months
years
Choose the correct multiplier
Same time in smaller units
# 12
Be careful with changing multipliers for time conversions needing two or more steps.
(ii) 7200 seconds into hours
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hours
7200 ' 60 ' 60 = 120 ' 60 hours
= 2 hours
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TOPIC
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Time Calculations
Mathletics Passport
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Same time in hours
Your Turn
Time Calculations
1 min
[seconds]
#
c
20 years
'
e
3 weeks
#
g
2
OF T I
seconds
[decades]
h
centuries
[weeks]
weeks =
#
[weeks]
weeks =
centuries =
4 years
days
hours
[centuries]
'
f
days =
hours =
30 decades
decades
[days]
[hours]
#
d
decades =
1 day
730.5 days
weeks
weeks
[years]
years =
'
years
Use two steps to convert these time measurements into the units given in square brackets.
a
28 days
'
c
2 decades
#
e
g
[fortnights]
'
1 century
#
b
=
'
=
=
#
#
28 800 seconds
days
672 hours
months
seconds
=
hours
[hours]
'
h
=
[hours]
#
f
[months]
#
1 week
months
[days]
[seconds]
#
d
=
#
1 hour
fortnights
[months]
4320 minutes
'
3
seconds =
2 1 fortnights
2
#
b
EN UNI
a
h
min
s
TS
Convert these time measurements into the units given in square brackets.
NG BE
T
1
GI
Changing between units of time
* CHA
..
N
20..
...../
...../
ME
WE
How does it work?
'
'
hours
=
[weeks]
'
weeks
=
Change these time measurements into the bracketed units.
a
1.5 hours
[mins] b
330 seconds
c
2 1 days
2
[hours] d
1.8 years
e
408 seconds
f
1 2 decades
5
[months] g
7.12 fortnights
h
126 seconds
[hours] [mins] [days]
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[mins] [weeks] H 11
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5
How does it work?
Your Turn
Time Calculations
Changing between units of time
4
To change between months and days/weeks, you first need to change the time interval into years.
Change these time measurements into the bracketed units.
a
15 months
[weeks]
'
`
c
weeks =
8.4 months
weeks
`
d
months =
913 1 days
8
days
`
#
months
[months]
'
days .
#
years
=
#
years
=
[months]
'
[days]
'
13 weeks
years
=
#
`
b
years
=
months =
months
to nearest whole day
5
Change these time measurements into the bracketed units.
Write answers as recurring decimals and then round to 2 d.p.
a
320 seconds
'
[minutes]
minutes
minutes c
=
8 year
9
b
[months]
#
minutes
=
to 2 d.p.
c
6
1 2 hours
5
months c
months
to 2 d.p.
[days]
d
2 1 years
3
[weeks]
Earn an awesome passport stamp for this last one.
How many minutes has a student who has just celebrated their 12 th birthday lived for?
..
/20..
.
.
.
.
.
/
.....
6
months
H 11
SERIES
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Time Calculations
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How does it work?
Time Calculations
Decimal time periods
When a period of time is described as 1.5 hours, you probably know that it means 1 hour and 30 minutes.
What if a period of time is described as 1.65 hours? How many minutes past 1 hour is this?
Here is a simple way to find out:
1.65 hours =
1 hour + 0.65 hours
Split decimal time into whole and decimal parts
= 1 hour + 0.65 # 60 minutes
Because there is 60 minutes in 1 hour
= 1 hour + 39 minutes
= 1 hour and 39 minutes
Change ‘+’ to ‘and’
So just multiply the decimal part by 60 to find out how many minutes it represents.
Here are some more examples
(i) How many hours and minutes does 0.95 hours represent?
0.95 hours =
0 hours + 0.95 hours
Split decimal time into whole and decimal parts
= 0 hours + 0.95 # 60 minutes
Because there are 60 minutes in 1 hour
= 0 hours and 57 minutes
Use the same method to calculate the total number of minutes and seconds.
(ii) How many minutes and seconds are there in 3.82 hours?
3.82 hours =
3.82 # 60 minutes
Because there are 60 minutes in an hour
= 229.2 minutes
= 229 minutes and 0.2 # 60 seconds
Because there are 60 seconds in a minute
= 229 minutes and 12 seconds
To write a period of time as a decimal, just do the opposite. Divide by 60.
(iii) Write four hours and twenty four minutes as just hours in decimal form.
4 hours and 24 minutes = 4 hours + 24 ' 60 hours
Because 1 hour has 60 minutes in it
= 4 hours + 0.4 hours
= 4.4 hours
Number of hours in decimal form
Time Calculations
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H 11
SERIES
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7
Time Calculations
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DECIMAL
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P ERI O
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1.21 hours
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minutes
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=
minutes
=
minutes +
minutes
=
minutes +
#
=
minutes and
seconds
seconds
12 hours and 32 minutes
=
hours +
=
hours +
b
hours
'
hours
hours to 2 d.p.
.
minutes
#
minutes
0.73 hours
minutes
=
#
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minutes
=
minutes +
minutes
=
minutes +
#
=
minutes and
seconds
seconds
8 hours and 4 minutes
=
hours +
=
hours +
.
hours
'
hours
hours to 2 d.p.
Change each of these into the units shown in square brackets, showing all your working.
a
8
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Complete these calculations to write time period in hours as a decimal (accurate to 2 d.p.).
a
4
minutes
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hours and
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=
minutes
#
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hours +
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Complete these calculations to write each time period in minutes and seconds.
a
3
b
=
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2
3.2 hours
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Complete these calculations to write each time period in hours and minutes.
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Decimal time periods
TI
E C I M AL
*D
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Your Turn
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1.3 hours [hours and minutes]
H 11
SERIES
TOPIC
b
2.45 hours [hours and minutes]
Time Calculations
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How does it work?
Your Turn
Time Calculations
Decimal time periods
5
Change each of these into the units shown in square brackets, showing all your working.
a
2 hours 54 minutes
[hours]
b
4 minutes 27 seconds
[minutes]
These changes can be made very quickly and easily using a scientific calculator
We can use the degrees, minutes and seconds button o , ,, or DMS to enter times into the calculator.
(i) Write 2 hours and 35 minutes in hours
2 hrs and 35 mins is entered as: 2 o , ,, 35 DMS
The display will look something like:
=
2c 35l 0m
hours
minutes
seconds
Press the degrees, minutes and seconds button o , ,, to switch between both forms.
` 2c 35' 0" = 2.583o hours
To split a decimal into hours, minutes and seconds, enter the decimal and press o , ,, .
(ii) How many hours, minutes and seconds are there in 8.47 hours?
Press 8
.
4
=
7
to put the value 8.47 into the calculator
Now press o , ,, to get 8c 28' 12"
hours
minutes
seconds
` 8.47 hours equals 8 hours, 28 minutes and 12 seconds
6
7
Use your calculator to change each of these time periods into hours in decimal form.
a
5 hrs 36 mins =
hrs
b
0 hrs 45 mins =
hrs
c
1 hr 42 mins =
d
6 hrs 15 mins =
hrs
e
3 hrs 58 mins =
hrs
f
2 hrs 26 mins =
hrs
hrs
Use your calculator to find how many hours, minutes and seconds are in the following decimal times.
a
3.62 hrs =
c
1.585 hrs =
hrs
hrs
min
sec
min
sec
b
5.28 hrs =
d
9.7o hrs =
Time Calculations
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hrs
hrs
min
sec
min
sec
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How does it work?
Time Calculations
12 hour time
Each calendar day has a total of 24 hours in it.
The 12 hour method of telling the time divides this into two equal periods:
• a.m. (Latin for ante meridiem, which basically means ‘before midday’)
• p.m. (Latin for post meridiem, which basically means ‘after midday’)
The letters a.m. or p.m. need to be included after the time to ensure it is communicated correctly.
• Midday (also called noon) is referred to as 12:00 p.m. or 12:00 noon.
• Midnight is referred to as 12:00 a.m.
Telling the time in English
Each hour (on the hour), the word o’clock (from ‘of the clock’) is used. For others we say:
• 'minutes past' for times within 30 minutes after the hour and,
• 'minutes to' for times within 30 minutes before the next hour.
ti on of the minute h
po s i
an
he
ti
o'clock
ur
cloc
Tell
ing
t
a
'5 past'
'5 to'
minute hand
hou
k
'10 past'
'10 to'
quarter
to
du
sin
g
o
-h
12
m
m
ro
ef
the
quarter
past
r ha
nd
'20 to'
'20 past'
'25 to'
'25 past'
half past
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© 3P Learning
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Time Calculations
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Mathletics Passport
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12 noon (midday)
or
12:00 pm
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20 to 7 am
or
6:40 am
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quarter to 10 am
or
9:45 am
am
Time Calculations
12 HO
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URS TIM
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Write the time displayed on each of these clock faces in two different ways.
HO
2 *
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...../...../20....
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I ME *
11 12 1
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9 AM|PM 3
8
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12 hour time
*
T
UR
E
IM
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Your Turn
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or
Shade in the digital displays below to match the times written in word form.
a
Twenty nine minutes past
six in the afternoon
b
Two o’clock in the morning
c
Quarter to five in the evening
e
Eight minutes past midnight
f
Eleven minutes to noon
pm
d
3
Half past ten at night.
Briefly describe the problem John has after receiving this message on his phone:
“Hi John, just letting you know we are going to meet at 9 o’clock for a quick game of basketball.”
Time Calculations
Mathletics Passport
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H 11
SERIES
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11
How does it work?
Time Calculations
24 hour time
Many cultures do not split the 24 hour day into two equal groups, preferring to read times from 0 to 23.
th
de represent
utsi
t he
o
e
h
13
14
22
15
20
16
19
18
aft er noon
.
21
m es
r ti
23
hundred
24
ou
numbers a
rou
The
nd
In some areas of work where clear communication of the time is important (such as emergency services
and military), 24 hour time is used so there can be no confusion between am or pm times.
17
All 24-hour times have four digits. This table shows some comparisons between some 12 and 24 hour times.
12 hour
time
24 hour
time
Word form
Word form
9:15 am
Quarter past nine am, or nine-fifteen am
0915
Zero nine fifteen
7:00 am
Seven o'clock am, or just seven am
0700
Zero seven zero zero ( or zero seven hundred)
11:45 am
Quarter to twelve am
1145
Eleven-forty five
12:00 pm
Twelve o'clock pm, or noon/midday
1200
Twelve zero zero
1:05 pm
Five past one pm
1305
Thirteen zero five
6:20 pm
Twenty past six pm, or six-twenty pm
1820
Eighteen twenty
12:00 am
Twelve o'clock am, or midnight
0000
Zero zero, zero zero (or zero zero hundred)
12:10 am
Ten past twelve am, or twelve-ten am
0010
Zero zero ten
• 24 hour time is usually described using the first pair of numbers followed by the second pair.
• 24 hour times can be written with a colon (19:00) or without (1900).
• We include the word ‘oh’ or ‘zero’ for all pairings that have a zero first.
To change 24 hour time into pm 12 hour time, subtract 12 from the first two digits.
(i) 1545 (fifteen, forty-five)
15 45 = (15 - 12) : 45 pm
= 3:45 pm
Subtract 12 from 15 hours
(ii) 22:00 (twenty two zero zero)
22:00 = (22 - 12) : 00 pm
= 10:00 pm
Subtract 12 from 22 hours
To go the other way, just do the reverse and add 12 to the hours in pm time
(iii) 6:28 pm
12
H 11
SERIES
TOPIC
6:28 pm = (6 + 12) : 28
= 18:28
Time Calculations
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Add 12 to the pm hours
Eighteen twenty eight
How does it work?
Your Turn
Time Calculations
4 H OUR
* 2 4 HOUR TTIM
E *2
IM
a
d
d
Seventeen-twenty
after noon
after noon
after noon
before noon
before noon
before noon
Zero nine thirty
Thirteen forty one
e
f
Zero fifty five
after noon
after noon
after noon
before noon
before noon
before noon
b
10:30
c
1400
03:45
pm
pm
pm
am
am
am
e
1320
f
11:35
0015
pm
pm
pm
am
am
am
Write each of these 12 hour times in 24 hour time.
a
7:15 am
b
10:20 am
c
4:55 am
d
8:32 pm
e
12:00 pm
f
11:18 pm
g
12:45 am
h
12:05 am
Write the time displayed on each of these clocks in 24 hour time.
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© 3P Learning
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Time Calculations
Mathletics Passport
PM
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c
Write each of these 24 hour times in 12 hour time.
a
3
Zero six zero zero
b
l
2
Fourteen zero zero
...../.. ....
.../20
E
Write down the 24 hour time for each of these and tick whether it is a
time before or after noon.
24 HOUR
* 4 HOUR TTIM
E *2
IM
1
E
24 hour time
E
E
24 H O U R
* 4 HOUR TTIM
IM
E *2
4 H O UR
* 2 HOUR TTIM
E * 24
IM
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H 11
SERIES
TOPIC
13
Where does it work?
Time Calculations
Time duration
Calculating the time duration between two times is a great skill to have for many reasons:
So you can:
• know how long you have until the next public transport vehicle arrives.
• calculate the time difference between two cities or countries,
• work out how long it took you to travel between two places,
• calculate how long you have been working on a job so you get paid the right amount.
For example:
If the time is 10:40 am, how long does Carly have until her flight leaves at 2:15 pm?
10:40 am
1:40 pm
2:15 pm
35 min
3 hrs
30
45
11:00
15
30
am
45
12:00
15
30
45
1:00
pm
15
30
45
pm
2:00
15
30
pm
Time interval = 3 hours + 35 minutes
= 3 hours and 35 minutes
` Carly has 3 hours and 35 minutes (or 3.583o hours) until the flight leaves.
Calculate these questions involving time duration:
(i) Time interval between 09:45 and 14:55
Earlier time = 09:45, ` 5 hours until 14:45
How many whole hours between time?
Later time = 14:55, ` 10 minutes past 14:45
How long past 4 hour mark?
Time interval = 5 hours + 10 minutes
Add hours and minutes together
= 5 hours and 10 minutes
0945
1455
14:45
5 hrs
1000
1100
1200
1300
1400
10 min
1500
The time duration can be used to calculate a future or past time.
(ii) If the time is 11:15 pm now, what time is it in 3 hours and 40 minutes?
11:15 min
10:00 pm
11:00 pm
3 hrs
12:00 pm
1:00 am
Time = 2:15 am + 40 minutes
H 11
SERIES
TOPIC
2:00 am
3:00 am
3 hours later + 40 minutes
= 2:55 am tomorrow
14
40 min
Include change of day if needed
Time Calculations
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Where does it work?
Your Turn
Time Calculations
Time duration
1
Use the time line to calculate the time duration between each pair of 12-hour times given below.
12 hr
30 45
15 30 45
10 am
a
15 30 45
11 am
b
15 30 45
3 pm
e
min.
hrs and
15 30 45
6 pm
15 30 45
7 pm
15 30
8 pm
1:15 pm and 4:30 pm
c
hrs and
11:20 am and 5:25 pm
min.
15 30 45
5 pm
9:45 am and midday
hrs and
11:30 am and 3:45 pm
15 30 45
4 pm
min.
10:05 am and 1:55 pm
f
min.
hrs and
min.
Use the time line to calculate the time duration between each pair of 24-hour times given below.
24 hr
30 45
15 30 45
08:00
a
15 30 45
09:00
d
15 30 45
10:00
09:15 and 13:00
hrs and
15 30 45
11:00
b
min.
min.
15 30 45
12:00
15 30 45
13:00
15 30 45
14:00
10:45 and 14:15
15 30 45
15:00
c
hrs and
e
1415 and 1530
hr and
3
15 30 45
2 pm
min.
hrs and
2
15 30 45
1 pm
2:45 pm and 7:15 pm
hrs and
d
15 30 45
12 am
15 30
18:00
hrs and
f
hrs and
15 30 45
17:00
07:30 and 11:15
min.
1225 and 1435
15 30 45
16:00
min.
1541 and 1732
min.
hr and
min.
Calculate the time duration between these pairs of times, showing all working.
a
3:38 am and 6:19 am
b
11:52 pm and 1:44 am
c
1247 and 2308
d
0913 and 1248
Time Calculations
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H 11
SERIES
TOPIC
15
Your Turn
Time Calculations
12 hr
30 45
15 30 45
7 am
5
DUR A TI
O
15 30 45
9 am
15 30 45
10 am
15 30 45
11 am
15 30 45
12 pm
15 30 45
1 pm
15 30 45
2 pm
15 30 45
3 pm
15 30 45
4 pm
15 30
5 pm
a
Four hours and forty five minutes later.
b
Two hours and fifteen minutes later.
c
Three hours and five minutes earlier.
d
One hour and fifteen minutes earlier.
e
Five and a quarter hours later.
f
90 minutes earlier.
If the time now is 2215, calculate the new time (including today/tomorrow) for these time durations:
12 hr
30 45
15 30 45
7 am
6
15 30 45
8 am
...../...../20....
E
IM
If the time now is 10:30 am, calculate the new time for these time durations:
R A T I ON * T
4
A
ON * TIME
Time duration
TIME DUR
TI
N*
DU
Where does it work?
15 30 45
8 am
15 30 45
9 am
15 30 45
10 am
15 30 45
11 am
15 30 45
12 pm
15 30 45
1 pm
15 30 45
2 pm
15 30 45
3 pm
15 30 45
4 pm
15 30
5 pm
a
One hour and thirty minutes later.
b
Five hours and fifteen minutes later.
c
Four hours and twenty minutes earlier.
d
Two hours and fifty five minutes earlier.
e
One and three quarter hours earlier.
f
One hundred and fifty six minutes later.
Earn an awesome passport stamp with this one.
If the time now is 4:35 pm, what is the total time duration between the time that occurred two hours
and forty minutes earlier and the time that will occur 348 minutes before midnight?
OM E
E * AW E S
ES
O
* AW
ME
* AWE
SO
WE
* A
16
H 11
SERIES
TOPIC
Time Calculations
Mathletics Passport
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ME
S OM
...../...../20....
Where does it work?
Time Calculations
Time duration on a calculator
Time duration calculations can also be performed easily using a scientific calculator.
For example: How long is it between 5:52 am and 7:23 am?
7:23 - 5:52 = 7 o , ,, 23 o , ,,
-
5 o , ,, 52 o , ,,
=
The displayed answer of: 1c 31l 0m means 1 hour and 31 minutes
hours
minutes
seconds
A little thinking is needed if the two times are on either side of noon (12:00 pm) or midnight (12:00 am).
Here are some examples showing you what to do when this happens.
Use your calculator for these time duration calculations
(i) How long is it between 8:52 am and 2:15 pm?
If we just do 2:15 pm – 8:52 am, we will get an incorrect, negative answer.
For times on either side of midday, just enter their 24 hour equivalents into the calculator.
2:15 pm - 8:52 am =
1415 - 0852
= 14
o , ,,
15
Change to 24 hour times
o , ,,
-
8
o , ,,
52
o , ,,
=
Split times into two pairs of numbers
= 5c 23l 0m
= 5 hours and 23 minutes
Time between 8:52 am and 2:15 pm
For times on either side of midnight (12:00 am), we do the same for both 12 hour and 24 hour times
(ii) How long is it between 9:20 pm and 3:22 am the following day?
12:00 am - 9:20 pm = 12
o , ,,
00
o , ,,
-
9
o , ,,
20
o , ,,
=
Time between 9:20 pm and 12:00 am
= 2 hours and 40 minutes
Now, 3:22 am = 3 hours and 22 minutes past midnight
` Time difference = 2 hours + 3 hours + 40 minutes + 22 minutes Add time differences together
= 6 hours and 2 minutes
(iii) What will the time be eight hours and twenty two minutes after 6:27 am?
` 6:27 am + 8 hours and 22 minutes = 6
o , ,,
27
o , ,,
8
o , ,,
22
o , ,,
=
= 14c 49l 0m
Past midday (in 24 hour time)
= 2:49 pm
Changed back to 12 hour time
Time Calculations
Mathletics Passport
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H 11
SERIES
TOPIC
17
Where does it work?
Your Turn
Time Calculations
Time duration on a calculator
2
a
7:25 am and 8:56 am =
c
5:56 pm and 11:04 pm =
hrs
min
hrs
min
b
6:34 am and 8:56 am =
hrs
min
d
2:14 am and 9:12 am =
hrs
min
Use a calculator to find the time duration between each of these 24-hour times:
a
0536 and 0909 =
c
10:45 and 15:23 =
hrs
min
hrs
min
b
0645 and 1324 =
d
03:05 and 22:24 =
hrs
min
hrs
min
Use a calculator to find the time duration between each of these mixed times:
hrs
min
b
21:12 today and 02:12 tomorrow =
hrs
min
c
19:17 today and 00:00 tomorrow =
hrs
min
d
12:00 pm today and 10:51 am tomorrow =
hrs
min
e
9:45 am today and 0203 tomorrow hrs
min
R * T IM E D U
TO
R
LA
ON A C A L
ON
I
AT
R * TIME DU
R
Use a calculator to find the time before/after these given time durations and shade in the clock display:
a
b
c
18
TO
4
=
...../...../20....
N ON A CALC
U
=
IO
10:27 am today and 1:11 pm today AT
a
CU
3
Use a calculator to find the time duration between each of these 12-hour times:
LA
1
4:30 am
11:18 am
08:41
H 11
SERIES
TOPIC
(i) Five hours and fifteen minutes later.
Today
Tomorrow
(ii) Three hours and fifty two minutes earlier.
Yesterday
Today
(i) Nine hours and fifty six minutes later.
Today
Tomorrow
(ii) Twelve hours and fifty two minutes earlier.
Yesterday
Today
(i) Seven hours and thirteen minutes later.
Today
Tomorrow
(ii) Eleven hours and eighteen minutes earlier.
Yesterday
Today
(iii) Sixteen hours and twenty five minutes earlier.
Today
Tomorrow
Time Calculations
Mathletics Passport
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Where does it work?
Your Turn
Time Calculations
Time duration on a calculator
In the maze below, there are gaps with directions whenever the
5
symbol appears.
Whenever you reach a gap in this maze, continue along the path with the time closest to midday.
Match the letters you go through with the Roman numerals below to answer this:
What is the name given to the unique internal clock all our bodies have?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
Time Calculations
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(x)
(xi)
(xii)
(xiii)
(xiv)
H 11
SERIES
TOPIC
(xv)
19
Where does it work?
Time Calculations
Timetables
Many forms of public transport run according to a timetable (also called a schedule).
Interpreting timetables correctly helps us waste less time waiting around.
A typical format for timetables is with arrival times listed in line horizontally besides the name of each stop.
Use the Matheltics Express timetable to answer these questions
(i) How long does the 10:46 am train from Wycliffe station take to reach Blue Creek station?
Time taken = time at Blue Creek station - time at Wycliffe station
= 11:04 am - 10:46 am
Time train is at each stop
= 18 minutes
(ii) If the 10:51 am train from Jindaree is cancelled, what is the next earliest time you can arrive
in Adeledin?
• Next train leaves Jindaree at 11:06 am
• This train does not stop at Adeledin, so need to get off at Tree Valley.
• The next train from Tree Valley (11:42 am) arrives at Adeledin at 11:48 am
` 11:48 am is the next earliest time you can arrive at Adeledin.
(iii) What is the difference in travel time for the 11:08 am and 11:42 am trains from Tree Valley
to West Sands?
Time taken= time at West Sands station - time at Tree Valley station
` for 11:08 am train= 11:20 am - 11:08 am
= 12 minutes
for 11:42 am train= 11:58 am - 11:42 am
= 16 minutes
` The 11:42 am service has 4 minutes less travel time.
20
H 11
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Time Calculations
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Where does it work?
Your Turn
Time Calculations
Timetables
1
Use this section of a timetable for the 358 bus route service to answer the questions below.
PERS
PECT
IVE
BUS
CO
P
STO
o
BUS
Com
East
t.
rp S
Sha
t
rcui
e Ci
s
o
R
rden
a Ga
e
T
St.
Cow
Rich
)
rrive
n (a
o
Sta
art)
ster
(dep
Che
St.
way
Rail
n Rd
iqui
l
i
n
De
St.
Sky
on
Junc
e
n
o
st
here
Key
stop
t
o
n
oes
us d
b
s
ean
ROUT
E
358
AM
8:25
8:30
8:33
8:35
8:39
8:42
8:52
8:54
8:59
9:03
9:08
AM
8:40
8:47
8:53
9:03
9:08
9:15
AM
9:00
9:05
9:08
9:10
9:14
9:17
9:27
9:29
9:34
9:38
9:43
AM
9:35
-
9:40
-
9:43
-
9:45
-
9:49
9:28
9:38
9:40
9:45
9:49
9:54
All buses
-m
AM
-
9:51
10:01
10:06
10:13
stop for 1
0
AM
AM
9:50
10:05
-
10:10
-
10:13
9:57
10:15
10:03
10:13
10:18
10:25
min at Ch
10:19
10:22
10:32
10:34
10:39
10:43
10:48
ester Stati
on
a
Calculate the total time taken for an all-stops bus to travel from East Como to Keystone Junction.
b
Describe two ways (including the departure and arrival times) a person can plan a bus trip from
Rose Circuit to Deniliquin Rd, arriving between 10:00 am and 10:30 am.
c
A time delay in one bus service affects the times of all the following buses by the same amount.
The 9:00 am bus from East Como is delayed 23 minutes due to mechanical problems.
What time will people at the Rich Street stop get on the bus that leaves East Como at 9:35 am?
d
How much travelling time is saved when you catch the 9:57 am bus from Cow Tea Gardens to
Keystone Junction instead of the 10:15 am bus between the same two stops?
Time Calculations
Mathletics Passport
© 3P Learning
H 11
SERIES
TOPIC
21
Where does it work?
Your Turn
Time Calculations
Timetables
2
Show all working when you answer the questions about the Delmont Bay ferry service shown here:
Delmont Bay Ferry Service Timetable
Desnaon
Delmont Interchange
0810
0825
0910
0925
1000
1030
1135
1140
1235
1240
1330
Greenwich
0822
0837
0922
0937
1015
1042
1147
1152
1247
1252
1345
Parrot Island
0831
0846
0931
0946
-
1051
1156
1201
1256
1301
-
-
0900
-
1000
-
1115
-
1215
-
1315
-
0849
-
0949
-
1053
-
1214
-
1314
-
1423
-
0920
-
1020
-
1135
-
1235
-
1335
-
Water Park
0902
0938
1002
1038
-
1153
1227
1253
1327
1353
-
Pier Eight
0910
-
1010
-
-
-
1235
-
1335
-
-
Docklands
Shark’s Ponds
Oyster Bay
Church Rock
-
0948
-
1048
-
1203
-
1303
-
1403
-
Calamity Island
-
-
-
-
1123
-
-
-
-
-
1453
Pelican Island
-
-
-
-
1155
-
-
-
-
-
1525
Pontoon Palace
0921
1005
1021
1105
1230
1220
1246
1327
1346
1427
1600
Birch Point
0935
1019
1035
1119
1244
1234
1300
1341
1400
1441
1614
Delmont Interchange to Birch Point Services:
22
via Pier Eight
via Oyster Bay
via Calamity & Pelican Island
a
What is the latest time a ferry can be caught from Greenwich to reach Birch Point before 13:00?
b
How long does the Ferry which travels via Oyster Bay take to travel from Delmont Interchange
to Birch Point?
c
Which ferry service moves passengers between Shark Ponds and Pontoon Palace the quickest
and by how much time?
d
When each ferry reaches Birch Point, it stays there for fifteen minutes before travelling back to
Delmont Interchange along the same route. If the time taken to travel between each stop on the way
back is the same as the way out, what time will the 1249 ferry from Birch Point reach Docklands?
e
How long does the ferry driver of the Calamity and Pelican island services spend travelling in
total for one complete round trip? psst: don’t forget the waiting time at Birch Point.
H 11
SERIES
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Time Calculations
Mathletics Passport
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Where does it work?
Your Turn
Time Calculations
Timetables
This timetable shows the flight times for a courier service between four airports on weekdays.
Pyke City
5:05 am
7:40 am
2:45 pm
10:45 am
8:45 pm
Mount Shabul
Kraken
9:00 am
11:15 am
12:15 am
2:45 pm
12:00 pm
10:40 am
8:25 am
7:25 am
4:55 am
1:30 pm
2:50 pm
5:05 pm
6:05 pm
8:35 pm
6:00 pm
4:20 pm
2:05 pm
1:05 pm
10:35 am
TIMETABLES *
TIMETABLES *
South Star
How long does each flight stop for at Pyke City airport?
b
How long do flights between Mount Shabul and Kraken airports take?
c
Calculate the total time a plane spends in the air travelling between South Star and Kraken airports.
d
On a day where all planes are running on time, between which two airports will the 10:45 am
flight from South Star and the 4:55 am from Kraken pass each other?
e
The 4:55 am flight experiences poor weather conditions near Mount Shabul. This extends the
flight time between Kraken airport and Pyke City by one hour and fifteen minutes. The weather
also causes a 45 minute delay during the stop at Mount Shabul airport.
...../...../20....
TIMETABLES *
a
TIMETABLES *
3
a) What time will this plane arrive at Pyke City airport?
b) What time will this flight arrive in South Star if the stop over is shortened by 40 minutes to
make up time?
Time Calculations
Mathletics Passport
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H 11
SERIES
TOPIC
23
Where does it work?
Your Turn
Time Calculations
Timetables
4
Tidal charts are like timetables for the movement of the ocean sea levels. Answer the questions
below about the first two weeks of the tidal chart for Complex Cove.
COMPLEX COVE TIDAL CHART
DATE
AM
HIGH TIDES
Height (m)
PM
1 Thursday
2 Friday
3 Saturday
4 Sunday
5 Monday
6 Tuesday
7 Wednesday
11:31
2.65
00:29
00:52
01:27
02:05
02:48
2.74
2.71
2.68
2.62
2.56
11:46
12:05
12:36
13:06
13:39
14:16
14:57
8 Thursday
9 Friday
10 Saturday
11 Sunday
12 Monday
13 Tuesday
14 Wednesday
03:32
04:25
05:25
06:30
07:38
08:41
09:38
2.49
2.44
2.44
2.56
2.74
2.89
3.08
15:44
16:39
17:40
18:48
19:56
21:01
22:01
-
-
LOW TIDES
Height (m)
PM
Height (m)
AM
Height (m)
2.77
2.71
2.74
2.71
2.68
2.62
2.56
05:24
05:56
06:26
07:35
08:06
08:46
09:32
0.15
0.12
0.15
0.15
0.18
0.24
0.27
17:36
17:10
18:43
19:20
19:56
20:36
21:21
0.18
0.12
0.09
0.06
0.06
0.06
0.09
2.49
2.44
2.44
2.56
2.74
2.89
3.08
10:25
11:25
00:14
01:22
02:26
03:25
04:18
0.34
0.40
0.40
0.12
0.06
0.03
0.04
22:12
23:09
0.12
0.15
12:32
13:41
14:47
15:47
0.37
0.27
0.12
0.03
-
a
On Sunday 4 th , what time did the high tide occur after the low tide at 07:35?
b
When did the next low tide occur following the high tide at 17:40 on Saturday 10 th ?
c
How high was the high tide following the low tide height of 0.12 m on Thursday 8 th ?
d
How much time passed between the two high tides on Monday the 12 th ?
e
a) Calculate the time taken for the tide to change from low to high on Tuesday 13 th on
both occasions.
-
b) What is the average time taken for the tides to change from low to high on Tuesday 13 th ?
24
H 11
SERIES
TOPIC
Time Calculations
Mathletics Passport
© 3P Learning
What else can you do?
Time Calculations
Problems involving time duration
With your finely tuned skills in time calculations, problems can be solved involving time.
For example:
The Figtree fire unit received a call at 1525 to attend a fire 18 minutes drive away.
The unit took 5 minutes to get ready to leave, and put the small fire out in 22 minutes.
If they leave straight after extinguishing the fire, what time did they get back to the station?
Total time of events after receiving call =
5 minutes +
18 minutes
Drive time to fire
22 minutes
18 minutes
__________
Drive time to station
63 minutes
` 1 hour and 3 minutes
` time back at the station = 1525 + 1 hour and 3 minutes
= 1628
Problems can require operations other than add or subtract like in this example
A theatre company has booked a studio between 11:00 am and 5:00 pm to conduct auditions.
Each applicant has a maximum of 10 minutes to perform and then the judges discuss for 5 minutes
before the next audition begins.
How many auditions can the theatre company conduct in this time?
Total time per applicant = 10 + 5 minutes
= 15 minutes
Number of applicants per hour = 60 minutes ' 15 minutes
= 4 applicants per hour
Number of hours between 11 am and 5 pm = 6 hours
` 6 hours # 4 applicants= 24 applicants
` The theatre company can conduct a total of 24 auditions from 11:00 am to 5:00 pm
Time Calculations
Mathletics Passport
© 3P Learning
H 11
SERIES
TOPIC
25
What else can you do?
Your Turn
Time Calculations
Problems involving time duration
1
The next bus you want to catch arrives at the bus stop at 12:14 pm and leaves at 12:16 pm. The stop
is 12 minutes walk away from your front door. If you need to spend 5 minutes in a shop along the
way to buy a bus ticket, what is the latest time you can leave home so you just catch the bus?
2
A limousine driver needs to pick up a movie star from the airport at 6:15 pm.
Before he leaves he needs to spend 25 minutes washing the limousine and
then a further 10 minutes changing into his uniform.
The drive from home into the airport takes 45 minutes.
26
a
What is the latest time the driver should start doing these things so he
arrives at the airport on time?
b
The driver leaves for the airport twenty minutes ahead of schedule. What time does he leave?
c
On the way to the airport, he gets caught in a traffic jam which extends his journey by forty
five minutes. What time does the limousine driver arrive at the airport?
d
The flight bringing the movie star arrives thirty minutes late. Will she have to wait for the
driver? Show the calculations that support your answer.
H 11
SERIES
TOPIC
Time Calculations
Mathletics Passport
© 3P Learning
What else can you do?
Your Turn
Time Calculations
Problems involving time duration
3
Four and a half hours ago, midnight yesterday had occurred eight hours and twenty minutes earlier.
What time is it now?
4
How many complete songs averaging 4 minutes and 30 seconds can a DJ fit into a 2 hour show if
there are no gaps between each song?
5
Rocking Rob is asked at 13:25 to perform in place of a friend who is sick. The performance starts at
19:40 and he has to learn all 30 songs on the list.
If it takes Rocking Rob an average of twelve minutes to learn each tune, will he be able to
learn all 30 songs before the performance? Show all your calculations used.
b
How much time will Rocking Rob have left to get ready for his performance?
A school wants to fit an extra period into each day. At the moment, the timetable has five, 62
minute periods, a 10 minute roll call, a 25 minute recess and a 60 minute lunch break.
For this timetable to work, school starts at 8:30 am and finishes at 3:15 pm.
To make the new timetable work, the school changes the start time to 8:18 am and the finish time
to 3:25 pm. Roll call and lunch breaks remain the same length, but the recess break is shortened to
15 minutes.
How long will each period go for on the new six-period timetable? Show all your working.
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Time Calculations
Mathletics Passport
© 3P Learning
l
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H 11
SERIES
TOPIC
l
NG TIME D
VI
6
a
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27
What else can you do?
Time Calculations
Time Zones
When one side of the Earth experiences daylight, the other side experiences night.
The times on clocks in particular sections of the world need to match the stage of day/night each part is in.
So a time zone is just an area on the globe that has the same (or uniform) standard time.
11 10 9
8
7
6
5
4
3
1 GMT 1
2
2
4
5
6
7
8
9 10 11 12
Moscow
London
Ottawa
3
Paris
Tokyo
Islamabad
New York
Calcutta
Prime Meridian
Sydney
Wellington
Cape Town
WEST
1
2
3
4
<< Times earlier than GMT
5
6
7
8
Times later than GMT >>
Coordinated Universal
Time (UTC) is a newer,
more accurate method
used to regulate clock
times around the world.
Look it up sometime!
EAST
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
The times in different sections are offset (changed) depending on how far away they are from an
imaginary line called the Prime Meridian.
The Prime Meridian is a longitude ( 0c ) that runs through the Royal Observatory in Greenwich, London.
So the time along this line is called Greenwich Mean Time (GMT).
Those sections of the globe to the west of this line have earlier times than GMT.
Those sections to the globe to the east of this line have later times than GMT.
Use the time zone map to answer these questions
(i) If the time in London is 2:00 pm, what time is it in Moscow?
Moscow lies east of London between the 2nd and 3rd time line, so is therefore GMT+2
` Moscow time = 2:00 pm + 2 hours
= 4:00 pm
(ii) If the time in Sydney is 1500, what time is it in Cape Town?
Cape Town lies 9 time zones West of Sydney, so is therefore 9 hours earlier than Sydney
` Cape town time = 1500 - 9 hours
= 0600
28
H 11
SERIES
TOPIC
Time Calculations
Mathletics Passport
© 3P Learning
Your Turn
Time Calculations
..
E ZO
N
TI M
../...../20..
...
*
2
When the time in London is 10:30 am, calculate what the time is in these cities:
a
Brazilia (GMT -3) c
San Diego (GMT -8) =
e
Darwin (GMT +9.5) =
am
=
pm
am
pm
am
pm
Fill in the missing time for these
a
The time in Abu Dhabi (GMT +4) =
b
The time in Santiago (GMT -4) =
c
The time in Osaka (GMT +9) =
d
The time in Istanbul (GMT +2) =
e
The time in French Polynesia (GMT -9.5) is
f
The time in Myanmar (GMT +6.5) is
b
Islamabad (GMT +5) =
d
Quebec (GMT -5) f
Wellington (GMT +12) =
x
3:10
am
pm
am
pm
am
pm
Z ON E S
1
N E S * TI
Time Zones
* TIM E
ZO
ES
ME
What else can you do?
am
pm
am
=
pm
am
pm
if the time in Perth (GMT +8) is 7:10 am
if the time in Pretoria (GMT +2) is 7:45 pm
if the time in Adelaide (GMT +9.5) is 1:25 am
am
pm
if the time in Nepal (GMT +5.75) is 8:30 pm
if the time in Rangoon (GMT +6.5) is 13:15
if the time in Newfoundland (GMT -3.5) is 18:20
3
Andrew lives in Melbourne Australia (GMT +10) and follows a football team that plays in the Italian
competition. If his team has a match starting at 3:45 pm in Rome (GMT +1), what time will he be
watching the game if broadcast live on television?
4
Harriet catches a plane at 1445 on Jan 10 th from Madras (GMT +5) to Madrid (GMT +1). If the
flight takes 13 hours, what time and date will she land in Madrid, local time?
5
Qian catches a plane at 8:00 pm on March 22nd from Kuala Lumpur (GMT +8) to Mexico City (GMT -6).
If the flight takes 10 hours, what time and date will she land in Mexico City, local time?
Time Calculations
Mathletics Passport
© 3P Learning
H 11
SERIES
TOPIC
29
What else can you do?
Time Calculations
Reflection time
Reflecting on the work covered within this booklet:
•What useful skills have you gained by learning how to perform time calculations?
•Write about one or two ways you think you could apply time calculations to a real life situation.
•If you discovered or learnt about any shortcuts to help with time calculations or some other cool
facts/conversions, jot them down here:
30
H 11
SERIES
TOPIC
Time Calculations
Mathletics Passport
© 3P Learning
Cheat Sheet
Time Calculations
Here is what you need to remember from this topic on time calculations
Units of time
These units of time relate to each other like this:
• 1 minute = 60 seconds
• 1 hour = 60 minutes
• 1 day = 24 hours
• 1 week = 7 days
• 1 year =
12 months
=52 weeks
• 1 decade = 10 years
• 1 century = 100 years
Converting between units of time
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# 60
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11 12 1
10 Days 2
9
3
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11 12 1
10 Hours 2
9
3
h
8
4
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10 Minutes 2
9
3
8 min 4
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# 24
# 60
' 52
'7
Days and weeks
'2
days
weeks
#7
' 26
years
fortnights
#2
# 26
# 52
' 12
Months and years
months
years
# 12
' 365.25
Days and years
days
' 10
years
# 365.25
decades
# 10
Time Calculations
Mathletics Passport
' 10
© 3P Learning
centuries
# 10
H 11
SERIES
TOPIC
31
Cheat Sheet
Time Calculations
Decimal time periods
Multiply the decimal part by 60 to find out how many minutes it represents.
6.45 hours =
6 hours + (0.45 # 60 minutes)
= 6 hours and 27 minutes
or
Enter 6.45 into the calculator and press the degrees, minutes and second button.
Press 6
.
4
=
5
to put the value 6.45 into the calculator
Now press o , ,, to get 6c 27' 00"
hours
'10 past'
quarter
to
quarter
past
'20 to'
23
14
21
15
20
16
19
'25 past'
18
half past
12 hour
time
13
22
'20 past'
'25 to'
hundred
hou
rt
im
17
24 hour
time
Word form
n.
noo
'10 to'
e represent the
24
mb
ers
a
'5 past'
clock
ti m
e
'5 to'
ro
o'clock
d
un
sid
out
the
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aft
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ur
ho
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f the minute ha
on o
nd
a1
th
ti
os i
ep
seconds
The nu
12 and 24 hour times
minutes
Word form
9:15 am
Quarter past nine am, or nine-fifteen am
0915
Zero nine fifteen
7:00 am
Seven o'clock am, or just seven am
0700
Zero seven zero zero ( or zero seven hundred)
4:45 pm
Quarter to five pm
1645
Sixteen forty five
Time durations
If the time is 10:40 am, how long does Carly have until her flight leaves at 2:15 pm?
10:40 am
1:40 pm
2:15 pm
35 min
3 hrs
30
45
11:00
am
15
30
45
12:00
15
30
45
pm
1:00
15
30
45
2:00
pm
Time durations on the calculator
How long is it between 5:52 am and 7:23 am?
7:23 - 5:52 = 7 o , ,, 23 o , ,,
-
5 o , ,, 52 o , ,,
pm
=
The displayed answer of: 1c 31l 0m means 1 hour and 31 minutes
hours
32
H 11
SERIES
TOPIC
minutes
seconds
Time Calculations
Mathletics Passport
© 3P Learning
15
30
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