Teach GCSE Maths
Speed
Teach GCSE Maths
Speed
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© Christine Crisp
Suppose we travel 80 km in 1 hour.
At times we could be travelling very fast and
at others we might have stopped at traffic
lights.
Sometimes we will be accelerating and
sometimes slowing down.
However, from the information
that we travelled 80 km in 1 hour,
we can find the average speed.
The average speed is 80 km per hour.
If I travel the next 40 km in 1 hour my average
speed for this 2nd hour is halved to 40 km per hour.
The average speed for the journey is 60 km per hour.
We can use a graph to find the average speed.
1st
hour: 80 km
2nd hour: 40 km
40 km
80 km/h
40 km/h
80 km
1 hour
1 hour
If we draw a graph of distance and time, the
average speed is given by how steep the line is.
distance
average speed = time
distance
average speed = time
We can use this formula to find either:
speed if we know distance and time, or
distance if we know speed and time, or
time if we know distance and speed.
Tip: A way to remember this formula:
• Write d, s, and t in alphabetical order in a
“warning” triangle.
d
s t
distance
average speed = time
We can use this formula to find either:
speed if we know distance and time, or
distance if we know speed and time, or
time if we know distance and speed.
Tip: A way to remember this formula:
• Write d, s, and t in alphabetical order in a
“warning” triangle.
d
s t
Tip: Check the letters are in the
right order by noting the units
for speed.
e.g. km/h, kilometres over hours.
distance
average speed = time
We can use this formula to find either:
speed if we know distance and time, or
distance if we know speed and time, or
time if we know distance and speed.
Tip: A way to remember this formula:
• Write d, s, and t in alphabetical order in a
“warning” triangle.
d
For speed
time cover
distance
cover
cover
upupthe
up
thethe
t.s. d.
s t
The
triangle
givesover
d over
t
speed
isdistance
distance
over
time.
time
is
speed.
distance is speed  time
(distance over time).
e.g.2 Find the time taken, in minutes, to travel 30
miles at an average speed of 40 mph ( miles
per hour ).
d
Solution:
s t
30
distance time = 40 hour
time = speed
= 0·75 hour
Since the distance is in miles and the speed in mph,
the time is in hours. We will have to change it to
minutes.
Tell your partner how many minutes are in 0·75
( or three quarters ) of an hour. Ans: 45 mins
If we don’t recognise the answer, to change from
hours to minutes we multiply by 60.
e.g.3 Without using a calculator, find the distance
travelled on a trip that takes 20 minutes if the
average speed is 6 km/h.
Solution:
Without a calculator, if we have mixed units . . .
e.g.3 Without using a calculator, find the distance
travelled on a trip that takes 20 minutes if the
average speed is 6 km/h.
Solution:
Without a calculator, if we have mixed units . . .
it is often easier not to use the formula.
A speed of 6 km/h means 6 km travelled in 1 hour
( or 60 minutes ).
This is 1 km in 10 minutes or 2 km in 20 minutes.
The answer is 2 km.
SUMMARY
 We can use a warning triangle to find the formula
that links average speed, distance and time.
d
s t
letters in
alphabetical order,
distance
average speed = time
distance
time = speed
distance = speed  time
 If the units for speed are km/h, the units for
distance must be km and for time must be hours.
 Non-calculator problems are usually easier
without the formula.
EXERCISE
1. Find the average speed if a car travels a distance
of 220 km in 4 hours.
2. Find the distance walked in three and a half hours
at an average speed of 2 mph.
3. Find the time taken to run 5 km at an average
speed of 8 km/h. Give your answer in minutes.
4. Without using a calculator, find the average speed
for a journey of 10 miles in 15 minutes. Give your
answer in miles per hour.
EXERCISE
1. Find the average speed if a car travels a distance
of 220 km in 4 hours.
Solution:
distance
average speed = time
s t
= 220
4
= 55 km/hour
2. Find the distance walked in three and a half hours
at an average speed of 2 mph.
d
Solution:
d
s t
distance = speed  time
= 2  3·5
= 7 miles
EXERCISE
3. Find the time taken to run 5 km at an average
speed of 8 km/h. Give your answer in minutes.
Solution:
d
s t
distance
time = speed
= 5
8
= 0·625 hours
= 0·625  60 minutes
= 37·5 minutes
EXERCISE
4. Without using a calculator, find the average speed
for a journey of 10 miles in 15 minutes. Give your
answer in miles per hour.
Solution:
We need to find the distance travelled in 1 hour
( 60 minutes ).
We have the distance travelled in 15 minutes.
10 miles in 15 minutes
Doubling the numbers:
20 miles in 30 minutes
Doubling again:
40 miles in 60 minutes
The average speed is 40 mph.