Rates
Find unit rates and apply rates to solve problems involving speed, cost and other contexts.
Worked examples
Finding a unit rate
Straightforward
Problem
Mia pays for 8 apples. What is the cost per apple?
1
Identify the rate: a total cost for a number of items.
for apples
2
Divide the total cost by the number of items.
3
Write the unit rate.
The cost per apple is .
Answer
per apple
Applying a rate to find distance
Moderate
Problem
A car travels at 85 km/h for 4 hours. How far does it travel?
1
Identify the rate and the time.
Speed km/h, time h
2
Use the formula: distance = speed × time.
3
Substitute and calculate.
Answer
km
Comparing unit rates
Challenging
Problem
Shop X sells 4 bottles of juice for . Shop Y sells 6 bottles for . Which shop offers better value, and by how much per bottle?
1
Find the unit price at Shop X.
2
Find the unit price at Shop Y.
3
Compare the two unit prices.
, so Shop Y is cheaper.
4
Find the difference per bottle.
Answer
Shop Y by per bottle
Practise
Q1·Straightforward
5 pens cost . What is the cost per pen, in dollars?
Explanation
The cost per pen is .
Q2·Straightforward
A car travels 240 km in 3 hours. What is the speed in km/h?
Explanation
Q3·Straightforward
A printer prints 60 pages in 4 minutes. How many pages per minute does it print?
Explanation
Q4·Straightforward
A tap fills 45 litres in 9 minutes. What is the flow rate in litres per minute?
Explanation
Q5·Moderate
A car travels at 90 km/h for 3 hours. How many kilometres does it travel?
Explanation
Q6·Moderate
A plumber charges per hour. How much does she charge for 4 hours of work, in dollars?
Explanation
Q7·Moderate
Water flows into a tank at 15 litres per minute. How many minutes does it take to fill a 210-litre tank?
Explanation
Q8·Moderate
A recipe uses 300 mL of cream per serve. How many millilitres of cream are needed for 6 serves?
Explanation
Q9·Challenging
Store A sells 3 bottles of water for . Store B sells 5 bottles for . Which store has the cheaper unit price?
Explanation
Store A: per bottle
Store B: per bottle
Since , Store B is cheaper.
Store B: per bottle
Since , Store B is cheaper.
Q10·Challenging
A cyclist rides at 12 km/h for 30 minutes, then at 18 km/h for 20 minutes. What is the total distance in kilometres?
Explanation
Convert times to hours:
First part: km
Second part: km
Total: km
First part: km
Second part: km
Total: km
Q11·Challenging
A factory produces 180 items in 6 hours. How many items can it produce in 10 hours?
Explanation
Rate: items per hour
In 10 hours: items
In 10 hours: items
Q12·Challenging
A bus travels 280 km at 70 km/h. A train covers the same distance at 140 km/h. How many hours less does the train take than the bus?
Explanation
Bus: hours
Train: hours
Difference: hours
Train: hours
Difference: hours