Teach GCSE Maths

SpeeSpeedd

Teach GCSE Maths

SpeedSpeed

© Christine Crisp

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Suppose we travel 80 km in 1 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.

However, from the informationthat we travelled 80 km in 1 hour, we can find the average speed.

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.

The average speed is 80 km per hour.

The average speed for the journey is 60 km per hour.

If we draw a graph of distance and time, the average speed is given by how steep the line is.

We can use a graph to find the average speed.

80 km

1 hour

40 km

1 hour

80 km/h

40 km/h

1st hour: 80

km2nd hour: 40

km

average speed =

distancetim

e

average speed =

distancetim

eWe can use this formula to find either:

speed if we know distance and time, or

• Write d, s, and t in alphabetical order in a “warning” triangle.

ds t

Tip: A way to remember this formula:

distance if we know speed and time, ortime if we know distance and speed.

average speed =

distancetim

e

• Write d, s, and t in alphabetical order in a “warning” triangle.

ds t

Tip: A way to remember this formula:

Tip: Check the letters are in the right order by noting the units for speed. e.g. km/h, kilometres over hours.

dt

We can use this formula to find either:speed if we know distance and time, ordistance if we know speed and time, ortime if we know distance and speed.

For time cover up the t.

For distance cover up the d.

distance is speed time

For speed cover up the s.

average speed =

distancetim

eWe can use this formula to find either:

speed if we know distance and time, or

• Write d, s, and t in alphabetical order in a “warning” triangle.

ds t The triangle gives d over

t (distance over time).

Tip: A way to remember this formula:

distance if we know speed and time, ortime if we know distance and speed.

time is distance over speed.

speed is 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 ).

ds t

time = distancespeed

time = 30 40

Solution: hour

= 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

minsIf 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.Solutio

n: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.Solutio

n: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

ds t

average speed =

distancetim

e

We can use a warning triangle to find the formula that links average speed, distance and time.

letters in alphabetical order,

time = distancespeed

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.

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.

3. Find the time taken to run 5 km at an average speed of 8 km/h. Give your answer in minutes.

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.

Solution:ds t

average speed =

distancetim

e

= 55 km/hour

220 4

=

ds t

distance =speed time= 2 3·5

= 7 miles

Solution:

EXERCISE

3. Find the time taken to run 5 km at an average speed of 8 km/h. Give your answer in minutes.

ds t

= 0·625

hours

5 8

=

= 0·625 60 minutes

= 37·5 minutes

Solution:

time = distancespeed

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 have the distance travelled in 15

minutes.

20 miles in 30

minutes

40 miles in 60

minutes

Doubling the numbers:

Doubling again:

The average speed is 40

mph.

We need to find the distance travelled in 1 hour ( 60 minutes ).

10 miles in 15

minutes