year 8 maths

308 Chapter 5 Ratios and rates
Example 18
Solving rate problems
a Rachael can touch type at 74 words/minute. How many words can she type in 15 minutes?
b Leanne works in a donut van and sells, on average, 60 donuts every 15 minutes. How long is it
likely to take her to sell 800 donuts?
SOLUTION
a
74 words in 1 minute
×15 ×15
1110 words in 15 minutes
Rachael can type 1110 words in 15 minutes.
EXPLANATION
74
×15
370
+740
1110
b
60 donuts in 15 minutes
÷15
4 donuts in 1 minute
÷15
× 200 ×200
800 donuts in 200 minutes
Leanne is likely to take 3 hours and
20 minutes to sell 800 donuts.
Selling rate = 60 donuts/ 15 minutes
Divide both quantities by HCF of 15 .
Multiply both quantities by 200 .
Convert answer to hours and minutes.
Example 19
Solving combination rate problems
Three water hoses from three different taps are used to fill a large swimming pool. The first hose alone
takes 200 hours to fill the pool. The second hose alone takes 120 hours to fill the pool and the third
hose alone takes only 50 hours to fill the pool. How long would it take to fill the pool if all three hoses
are used?
SOLUTION
EXPLANATION
In 600 hours: LCM of 200, 120 and 50 is 600 .
Hose 1 would fill 3 pools . Hose 1 = 600 h ÷ 200 h/pool = 3 pools
Hose 2 would fill 5 pools . Hose 2 = 600 h ÷ 120 h/pool = 5 pools
Hose 3 would fill 12 pools . Hose 3 = 600 h ÷ 50 h/pool = 12 pools
Therefore, in 600 hours the three hoses together Together = 3 + 5 + 12 = 20 pools filled.
would fill 20 pools.
Filling rate = 600 hours for 20 pools
Simplify rate by dividing by HCF.
÷20 ÷20
30 hours for 1 pool
It would take 30 hours to fill the pool if all three
hoses are used.
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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