year 8 maths

320 Chapter 5 Ratios and rates
Example 25
Calculations from a distance–time graph
This distance–time graph shows Noah’s cycle journey
from home one morning.
a Find Noah’s speed in the first hour of the journey.
b How many minutes was Noah’s first rest break?
c Find Noah’s speed between 7:15 a.m. and 8:30 a.m.
d At what time did Noah start and finish his second
rest break?
e At approximately what time had Noah ridden a total
of 65 km?
f Find Noah’s speed on the return journey, to one
decimal place.
g What was Noah’s average speed for the whole
journey?
Distance from home (km)
50
40
30
20
10
0
6 a.m.7 a.m. 8 a.m.9 a.m.10 a.m. 11 a.m.
Time
SOLUTION
EXPLANATION
a 25 km/h The first hour is 6 a.m. to 7 a.m. Noah cycles
25 km in one hour.
b 15 minutes
The first horizontal line segment is at 7 a.m. to
7:15 a.m.
c s = d t
20 km
=
1.25 h
= 16 km/h
d 8:30 a.m. to 9:15 a.m.
Distance travelled = 45 km − 25 km
Time taken = 7:15 a.m. to 8:30 a.m. = 1.25 hours
A horizontal line segment shows that Noah is
stopped.
e 10 a.m. 45 km plus 20 km of the return trip or 25 km from
home.
f
s = d t
45 km
=
1.75 h
= 25.7 km/h
g s = d t
90 km
=
5 h
= 18 km/h
Distance travelled = 45 km
Time taken = 9:15 a.m. to 11 a.m. = 1.75 hours
distance travelled
Average speed =
time taken
Distance travelled = 2 × 45 = 90 km
Time taken = 6 a.m. to 11 a.m. = 5 hours
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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