Cambridge International Mathematics

226 Topics in arithmetic (Chapter 10)

11 Two cyclists are travelling side by side along a long straight

cycle track, one at 30 km/h and the other at 31 km/h. The

faster cyclist wishes to overtake the slower one, and will need

to gain 8 m relative to the slower cyclist in order to do this

safely. Find:

a the time taken for the faster cyclist to overtake the slower

cyclist

b the distance travelled by the faster cyclist in this time.

Suppose a car travels 150 kilometres in 1 : 5 hours.

Average speed =

distance

time

=

150

1 : 5

= 100km/h

Notice that the point A on the graph indicates we have

travelled 100 km in one hour.

Example 24 Self Tutor

The graph alongside indicates the distance a homing pigeon

travelled from its point of release until it reached its home.

Use the graph to determine:

a the total length of the flight

b the time taken for the pigeon to reach home

c the time taken to fly the first 200 km

d the time taken to fly from the 240 km mark to the

400 km mark

e the average speed for the first 4 hours

a Length of flight is 480 km.

b Time to reach home is 10 hours.

c Time for first 200 km is 212 hours.

d It takes 3 hours to fly 240 km. It takes 612 hours to fly 400 km.

) it takes 312 hours to fly from 240 km to 400 km.

e In the first 4 hours it flies 320 km ) average speed=

320

4

=80km/h.

H TRAVEL GRAPHS [1.13]

0

50

25

100

75

150

175

125

\Qw_1\ 1 Qw_ 2

distance (km)

time (hrs)

A

time (hours)

distance (km)

0369

480

400

320

240

160

80

IGCSE01

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100 100
Y:\HAESE\IGCSE01\IG01_10\226IGCSE01_10.CDR Wednesday, 24 September 2008 4:51:06 PM PETER