Time and Distance Formulas
Steve Tuckerman
11 th Grade Mathematics
Education page
What are Time and Distance formulas?

Time and Distance
Formulas relate time,
distance, and speed.
These relationships
have many practical
applications. Right
now, Jeff Gordon is
trying to decide how
fast he has to go to
pass Jimmie Johnson.
How to get around in this lesson



There will be a series of buttons to choose from.
Forward and backward buttons are located on the
bottom of the slide.
The home button returns you to the main menu
Quizzes have answer buttons. Click on the button
that you think is the right answer. Answer buttons
look like this:
Main Menu




Tutorial
Quiz One: Given rate and time, calculate
distance.
Quiz Two: Given distance and time, calculate
pace.
Quiz Three: Convert minutes per mile to
miles per hour.
Why do you need to know the Time and
Distance Formula?




To figure how long a trip
will take
To see how far you can
go in a set amount of
time
To see how fast you
took a trip
To compare different
trips
Steps in solving Time and Distance
Formulas

Step 1. Translate the
question into
mathematical terms.
For example, if you are
asked miles per hour,
write the question as
miles divided by hours.
Steps in solving Time and Distance
Formulas

Step 2. Put everything
in constant units. For
example, if the question
asks miles per hour,
every time must be
placed in terms of
hours, and every
distance must be
placed in terms of
miles.
Conversion Units


Remember: There are
60 seconds in a minute,
60 minutes in an hour,
and 24 hours in a day.
Remember: There are
12 inches in a foot, 3
feet in a yard, and 5280
feet in a mile.
Time Conversions






To convert minutes to hours, divide by 60.
To convert hours to minutes, multiply by 60
To convert seconds to minutes, divide by 60
To convert minutes to seconds, multiply by 60
To convert days to hours, multiply by 24
To convert hours to days, divide by 24
Measurement Conversions




To convert inches to feet, divide by 12
To convert feet to inches, multiply by 12
To convert feet to miles, divide by 5280
To convert miles to feet, multiply by 5280



Step 3. Write the
equation you want to
solve.
Use the correct formula
to solve it.
Be careful about what
you multiply, and what
you divide!
What are the basic formulas?




Distance = Rate * Time
(d = r * t)
Rate = Distance / Time
(r =d/ t)
Time = Distance / Rate
(t = d / r)
Be sure you use the
right formula!
To find distance

Distance = Rate * Time (d = r * t)
For example, to find miles, multiply miles per
hour (rate) times the number of hours.
Miles = Miles x Hours
Hours
The hours cancel, you are left with miles.
To find the rate of speed

Rate = Distance / Time
(r =d/ t)
To find miles per hour,
divide miles driven by
the number of hours
driven.
To find the time it takes to travel.

Time = Distance / Rate (t = d / r)
Hours = Miles_____
Miles/Hour
Remember, to divide fractions, flip and multiply
Hours = Miles x Hours
Miles
Miles cancel, you are left with hours
Quiz 1

How far can you go in
30 minutes at 55 miles
per hour? Bowser
wants to go skiing with
his friends.
Step one



Put in constant units
Rate was given in miles
per hour, so time must
be in hours
Remember, to convert
minutes to hours,
divide by 60
Question 1
What time should be used?

We are given 30
minutes. We want the
answer in hours.
Answer
 A. 2 hours
 B. 0.5 hours
 C. 30 hours


Nice try. Bowser’s
friends are still waiting.
Remember, to convert
minutes to hours,
divide by the number of
minutes by 60. You
divided by 15.

Nice try. Bowser’s
friends are still waiting.
You just changed
minutes into hours.

Nice job! The time is
one half hour, or 0.5
hours. Bowser goes
skiing with his friends.
Question 2




Now, how do you calculate how far you can
go?
A. Distance = 0.5 hours / 55 miles per hour
B. Distance = 0.5 hours times 55 miles per
hour
C. Distance = 55 miles / 0.5 hours
Remember the basic formulas!

Nice try. If distance
equals rate times time,
then you must multiply,
not divide.

Distance = Rate * Time
(d = r * t)
Question 3

Well done. You have the formula correct. Distance
equals rate times time, so distance equals 0.5 times
55, or 27.5
27.5 is in what units?
 A. Hours
 B. Miles
 C. Speed

Nice try. Remember, we
were talking about
miles per hour, so the
answer is in miles

Well done. You can go 27.5 miles in 30
minutes traveling at 55 miles per hour.

Are you ready for another quiz? If so, click
the right arrow
Quiz 2

Joan Benoit won the
1984 Olympic marathon
in 2 hours, 24 minutes,
and 52 seconds. If a
marathon is 26.22
miles, what was her
average pace in
minutes per mile?
Question 1




The first step is to put everything in constant
units. If it took Joan 2 hours, 24 minutes, and
52 seconds to run her race, and we are
interested in her pace in minutes per mile,
what is our first step?
Place everything in terms of hours
Place everything in terms of minutes
Place everything in terms of seconds

Nice try. We want to
know how many
minutes it took Joan to
run each mile, so we
need to know how
many minutes she was
running.

Well done. Since we want to know Joan’s
average pace in terms of minutes per mile,
we need to put everything in terms of
minutes.
Question 2

We know that Joan’s
time was 2 hours, 24
minutes, 52 seconds.
What formula gives us
the number of minutes?

Remember, to convert
hours to minutes,
multiply by 60. To
convert seconds to
minutes, divide by 60.
Everything has to be in
terms of minutes.



2 times 60 plus 24 plus
52
2 times 60 plus 24 plus
52/60
2 times 60 plus 24 plus
52/100
Remember, you are
converting 2 hours, 24
minutes, 52 seconds to
minutes.

Nice try. Remember, we want the answer in
minutes. To convert hours to minutes,
multiply by 60. To convert seconds to
minutes, divide by 60. You forgot to convert
seconds to minutes.

Nice try. Remember, we
want the answer in
minutes. To convert
hours to minutes,
multiply by 60. To
convert seconds to
minutes, divide by 60.
You divided seconds by
100.

Well done. The answer is 2 times 60 plus 24
plus 52/60. You multiply 2 hours times 60
minutes per hour, add the 24 minutes, and
add 52 seconds / 60 seconds in a minute. All
units are now in minutes. The correct answer
is 144.87 minutes
Question 3

What was Joan’s average pace per mile?
Remember, she ran 26.22 miles in 144.87
minutes.

144.87/26.22 = 5.525, or 5 minutes 31
seconds per mile
26.22/144.87 = .18 minutes per mile


Nice try. Remember, we wanted Joan’s pace
in minutes per mile. Therefore, you divide the
number of minutes she was running by the
number of miles she ran. You did it
backwards.

Well done. Joan’s average pace per mile in
the 1984 Olympic marathon was 5 minutes
and 31 seconds per mile. How far can you
run at that pace? Click the right arrow for the
next quiz.
Quiz 3

We know that Joan
Benoit ran the 26.22
mile Olympic marathon
at an average pace of 5
minutes and 31
seconds per mile. What
was her speed in miles
per hour?
Step one

First, we have to put
everything in constant
units. We are interested
in miles per hour, so we
need to convert
minutes to hours.
Question 1
How do you convert minutes to hours?



Multiply the number of minutes by 60
Divide the number of minutes by 60
Multiply by 24

Nice try. Remember, you have to divide the
number of minutes by 60. You multiplied by
60.

Nice try. You multiplied
by 24. You should have
divided by 60.
Question 2


Well done. There are 60 minutes in an hour,
so you divide the number of minutes by 60.
How do you convert 5 minutes and 31
seconds into hours?



A. Divide 5.31 by 60
B. First convert 31 seconds into minutes, add
to 5, then divide by 60
C. Multiply 5.31 times 24

Nice try. Remember, you need to convert
everything into minutes, so you have to
convert seconds into minutes. You forgot to
make this conversion.

Nice try. Remember,
you need to convert
everything to minutes.
You tried to convert to
days.
Question 3


Well done. First, convert the 31 seconds into
minutes. 31/60 = .52. Now, add the .52 to 5
minutes to get 5.52. Then, divide by 60. The
answer is .092. Joan ran each mile in .092
hours.
How do you convert one mile in .092 hours
into miles per hour?




1 mile divided by .092 hours equals x miles
divided by one hour
Cross multiply: 1 mile times 1 hour = .092
times x miles
X miles = 1/.092
X = 10.9 miles per hour.



Congratulations on
completing your first
lesson on time and
distance formulas.
Return to
education.html
To return to the
beginning, click here.