year 8 maths

324 Chapter 5 Ratios and rates
8 Draw a separate distance–time travel graph for each of these journeys. Assume each section of a
journey was at a constant speed.
a A motor bike travelled 200 km in 2 hours.
b A car travelled 100 km in 1 hour, stopped for 1 hour and then travelled a further 50 km in
2
1
2 hour.
c In a 90 minute journey, a cyclist travelled 18 km in 45 minutes, stopped for 15 minutes and
then returned home.
9 A train travels 5 km in 8 minutes, stops at a station for 2 minutes, travels 12 km in 10 minutes,
stops at another station for 2 minutes and then completes the journey by travelling 10 km in
15 minutes.
a Calculate the speed of the train in km/h (to one
decimal place) for each section of the journey.
b Explain why the average speed over the whole
journey is not the average of these three speeds.
c Calculate the average speed of the train in km/h (to
one decimal place) over the whole journey.
d On graph paper, draw an accurate distance–time
graph for the journey.
10 A one day, 20 km bush hike is shown by this graph of ‘total distance travelled’ versus time.
A bush hike
Total distance travelled
(km)
20
15
10
5
1
2
3 4 5 6 7 8
Time (hours)
a What were the fastest and slowest speeds (in km/h ) of the hikers? Suggest a feature of the
hiking route that could have made these speeds so different.
b Write a story of the journey shown by this graph. In your story, use sentences to describe the
features of the hike shown by each straight line segment of the graph, including the time taken
and distance travelled. Also include a sentence comparing the average speeds for the different
sections of the hike.
c
Suppose the hikers turn back after their 1 hour rest at 10 km and return to where they started
2
from. Redraw the graph above, showing the same sections with the same average speeds but
with ‘distance from start’ vs time.
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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