topic badge

4.01 Working with rates

Worksheet
Work with rates
1

Write the equivalent unit rate for each of the following:

a

72 kilometres in 9 hours

b

\$140 in 4 minutes

c

170 litres in 5 hours

d

92 toys in 2 days

e

336 calories over 4 kilometres

f

7980 rotations every 19\text{ km}

2

A car is travelling 60\text{ km/hr}. How far has it travelled after 7 hours?

3

There are 6 apartments per floor of a building. How many apartments are there over 11 floors?

4

In a library, there are 300 books per shelf. How many books are there on 3 shelves?

5

The volume of polyethylene used to create 10 plastic bags is approximately 4\text{ mL}. How much polyethylene is used to create 5 plastic bags?

6

Sixteen oranges can be fitted into a single carry bag. How many bags will be needed to carry 112 oranges?

7

The amount of pears that can fit in a plastic bag is 11 pears per bag. How many bags will be needed to carry 33 pears?

8

There are 224 tissues per box. If the manufacturer wastes 1120 tissues in production, how many boxes of tissues is this?

9

400\text{ L} of rain falls over a 2400 \text{ m}^2 field. How much rain falls over one quarter of the field to the nearest litre?

10

A worm takes 15 seconds to travel 25\text{ cm}. How long does it take the worm to travel a metre?

11

A film maker is stitching together frames for a movie. She stitches together 6 frames for every 0.25 seconds of the movie. What's the frame rate of the movie in frames per second?

12

The height of water in a pool increases by 0.2\text{ cm} for every litre of water added. If the height of water increases by 16\text{ cm}, how much water was added?

13

Consider the following rates:

a

A car travelling at S\text{ km/h} travels at a distance of D\text{ km} in T hours. Express S in terms of D and T.

b

A company that makes R dollars per hour earns A dollars in T hours. Express R in terms of A and T.

c

A printer can print S sheets of paper per minute. If it prints P sheets of paper in T minutes, express S in terms of P and T.

d

The rate at which cement is used to lay bricks for a house is C litres per brick. If V litres of cement is used to lay N bricks, express V in terms of N and C.

e

During a one hour exercise, the human body consumes R calories per kilogram. If a person weighs W\text{ kg} and consumes C calories, express W in terms of R and C.

f

A teacher can mark F exams per hour. If they mark N exams in T hours, express T in terms of F and N.

Convert rates
14

A bike travels 83 metres per 12 seconds. What is the speed of the bike in m/min?

15

Avril counts 13 heart beats over a 20 second interval. What is her heart rate in beats per minute (bpm)?

16

A cyclist travels 38 metres per 10 seconds. What’s the speed of the cyclist in m/min?

17

In an ice cream eating contest the winner eats 5.85 litres of ice cream in 6 minutes. What is the rate of consumption of ice cream in mL/s?

18

Gwen is trying to save money and deposits \$4.20 into her bank account for every 7 coffees she purchases. What is her rate of depositing in terms of cents per coffee?

19

A crabeater seal can filter 0.9 litres of water in each dive looking for food. They can stay under water for 30 minutes each dive.

a

What is the rate of water filtered in L/min?

b

What is the rate of water filtered in mL/min?

c

What is the rate of water filtered in mL/s?

20

A runner approximates the distance between two street lights as 23 metres. It takes him 5 seconds to run from one street light to the other.

a

What is the runner’s speed in m/min?

b

What is the runner’s speed in m/h?

c

What is the runner’s speed in km/h?

21

A cyclist counts 59 heart beats over a 30 metre distance. The cyclist’s smart watch says that her heart is beating at 118\text{ bpm}.

a

How long does it take the cyclist to cover the 30\text{ m} distance?

b

What is the cyclist’s speed in m/s?

c

What is the cyclist’s speed in m/min?

d

What is the cyclist’s speed in km/h?

22

A baby is weighed on his first birthday and found that he's gained 4.38\text{ kg} since he was born. Assume there are 365 days in a year.

a

What is the rate of growth in kilograms per day?

b

What is the rate of growth in grams per day?

c

What is the rate of growth in grams per hour?

23

The Earth completes one full rotation in a day. As it rotates, a particular point on the Earth moves 14\,850 kilometres in 12 hours.

a

What is the speed of the point on the Earth in kilometres per day?

b

What is the speed of the point on the Earth in km/h?

c

What is the speed of the point on the Earth in m/h?

d

What is the speed of the point on the Earth in m/s?

24

Convert:

a
3 \text{ m/s to m/min }
b
10 \text{ mL/min to mL/h }
c
\$0.50 \text{/g to } \$\text{/kg}
d
8 \text{ L/h to L/day }
e
4 \text{ L/min to mL/min }
f
3200 \text{ m/s to km/s}
g
2.5 \text{ m/h to cm/h }
h
12 \text{ kg/day to kg/h }
i
18 \text{ L/h to mL/min }
j
0.3 \text{ km/min to m/s }
k
7.2 \text{ tonnes/h to kg/s }
Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

MS2-12-3

interprets the results of measurements and calculations and makes judgements about their reasonableness, including the degree of accuracy and the conversion of units where appropriate

What is Mathspace

About Mathspace