year 8 maths

Puzzles and challenges
329
1 This diagram is made up of eight equal-sized squares.
How many squares need to be shaded if the ratio of shaded squares to unshaded squares is:
a 1 : 3? b 2 : 3? c 1 : 2?
2 Bottle A has 1 L of cordial drink with a cordial to water ratio of 3 : 7 . Bottle B has 1 L of cordial drink
with a cordial to water ratio of 1 : 4 . The drink from both bottles is combined to form a 2 L drink. What
is the new cordial to water ratio?
3 Brothers Marco and Matthew start riding from home into town, which is 30 km away. Marco rode at
10 km/h and Matthew took 20 minutes longer to complete the trip. Assuming that they both rode at a
constant speed, how fast was Matthew riding?
4 a If one person takes 1 hour to dig one post hole, how long will it take two people to dig two
post holes?
b If three people take 3 hours to make three wooden train sets, how many train sets can six people
make in 6 hours?
5 At a market you can trade two cows for three goats or three goats for eight sheep. How many sheep
are three cows worth?
Puzzles and challenges
6 Two cars travel toward each other on a 100 km straight stretch of road. They leave at opposite ends of
the road at the same time. The cars’ speeds are 100 km/h and 80 km/h . How long does it take for the
cars to pass each other?
Car 1
100 km/h
100 km
Car 2
80 km/h
7 A river is flowing downstream at a rate of 1 km/h . In still water Portia can swim at a rate of 2 km/h .
Portia dives into the river and swims downstream, then turns around and swims back to the starting
point, taking 0.5 hours in total. How far did she swim?
8 Henrik walks at 4 km/h for time t 1
, and then runs at 7 km/h for time t 2
. He travels a total of 26 km . If
he had run for the same time that he had walked (t 1
) and walked for the same time that he had run (t 2
) ,
then he would have travelled 29 km . What was the total time Henrik spent walking and running?
9 A top secret goo has been developed so that it doubles in volume every 60 seconds. At midnight a
small amount is placed in a beaker and its growth is observed. At 1 a.m. the beaker is full. At exactly
what time did the goo fill only 1 of the beaker?
8
10 A car averages 60 km/h for 20 km and then increases its speed, averaging 80 km/h for the next 20 km.
Calculate the car’s average speed (to two decimal places) for the full 40 km trip.
11 Shari travels at 50 km/h for 10 km. For the next 10 km she wants to drive fast enough to make her
average speed 100 km/h over the 20 km trip. Advise Shari about reaching this average speed.
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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