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Middle Years

3.03 Rates

Worksheet
Unit rates
1

Write the following as a unit rate:

a

1040 books per 13 libraries

b

91 people per 7 buses

c

234 kilometres per 4.5 hours

d

9 cakes per 72 guests

2

A plane burns 406 litres of fuel every 14 kilometres while in the air. Express the fuel consumption as a unit rate.

3

A toy manufacturer makes 165 toys in 5 hours. At what rate are the toys made per hour?

4

A tap fills up a 259 litre tub in 7 hours. Find the rate of water flow of the tap in litres per hour.

5

Luke earns \$328 in 8 hours. Find Luke's hourly rate.

6

Two shops sell pencil cases at the following prices:

  • 6 pencil cases for \$24 at Shop A

  • 9 pencil cases for \$54 at Shop B

a

Find the cost of a single pencil case at Shop A.

b

Find the cost of a single pencil case at Shop B.

c

Hence, which is the best place to buy pencil cases, if you want the best price per item?

7

Two shops sell mangos at the following prices:

  • 148 mangos for \$384.80 at Shop A

  • 252 mangos for \$453.60 at Shop B

a

Find the cost of a single mango at Shop A.

b

Find the cost of a single mango at Shop B.

c

Hence, which is the best place to buy mangos, if you want the best price per item?

8

Neville is deciding between four cars to buy. He wants to buy the most fuel efficient one.

a

Complete the following table:

CarLitres usedDistance travelled (km)L/km
\text{Magnum}13.40538.3
\text{Falcador}20.7154.5
\text{Canyonero}6.33619.2
\text{Civil}2.7548.1
b

Which car is the most fuel efficient?

Rate conversions
9

Consider the rate 192 metres per 240 seconds.

a

Express this is as a unit rate in terms of metres and seconds.

b

Express this is as a unit rate in terms of metres and minutes.

10

Vanessa is trying to save money and deposits \$5.60 into her bank account for every 8 coffees she purchases. Find her deposit rate in cents per coffee.

11

The admission for a concert starts at 6 pm and closes at 7 pm. If there are 900 people attending and they arrive at a constant rate, find the flow of people per minute.

12

A worm takes 20 seconds to travel 25\text{ cm}. How long does it take the worm to travel a metre?

13

A bike travels 83 \text{ m} per 12 seconds. Find the speed of the bike in m/min.

14

Convert the following rates:

a
6 \text{ L/h} to \text{ mL/h}
b
80 \text{ words/min} to \text{ words/h}
c
680 \text{ km/h} to \text{ m/h}
d
75 \text{ beats/min} to \text{ beats/h}
e
5.2 \text{ L/h} to \text{ mL/min}
f
25 \text{ m/min} to \text{ cm/sec}
g
500 \text{ mL/g} to \text{ L/kg}
h
800 \text{ cm/min} to \text{ m/h}
Applications
15

A plane is flying at an average speed of 360 km/hr. Find how far it will fly in:

a

20 minutes

b

12 minutes

16

In 2018, the birth rate in the United States was 13 people for every 1000 in the population. For a town with a population of 39\,000, how many births would you expect there to be in that year?

17

In 2018, the birth rate in Japan was 7 people for every 1000 population. For a town with a population of 39\,069, how many births would you expect there to be that year?

18

In 2018, the birth rate in Singapore was 9 people for every 1000 in the population. For a town with a population of 24\,176, how many births would you expect there to be that year?

19

In 2018, the population growth of Benin was 35 per 1000. This means that for every 1000 people, the number of people at the end of the year would be 1035. For a town with a population of 640, what would you expect the population to be at the end of the year?

20

In 2018, the population growth of Colombia was 8 per 1000. This means that for every 1000 people, the number of people at the end of the year would be 1008. For a town with a population of 95\,000, what would you expect the population to be at the end of the year?

21

In 2018, the literacy rate in Cuba was 98 people for every 100 in the population. For a town with a population of 83\,000, how many literate people would you expect?

22

In 2018, the literacy rate in Chad was 35 people for every 100 in the population. For a town with a population of 478, how many literate people would you expect?

23

On a road trip, Tracy drives with an average speed of 90\text{ km/hr} . How far does she travel in 8 hours?

24

Find the distance travelled by a car if it travels 60 \text{ km/hr} for 9 hours.

25

Find the time required for a car to travel 170 \text{ km} at a speed of 10 \text{ km/hr}.

26

An animator is drawing frames for an animated movie. He draws 6 frames for every 0.2 seconds. Find the frame's rate of the movie in frames per second (fps).

27

The height of a pool increases by 0.3 \,\text{cm} for every litre of water added. If the height of the pool increases by 6 \,\text{cm}, how much water was added?

28

In a library, there are 400 books per shelf. How many books are there in a row of 7 shelves?

29

There are 3 apartments per floor of a building. How many apartments are there over 8 floors?

30

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

31

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?

32

The volume of polyethylene used to create 81 plastic bags is approximately 18 \text{ mL}. How much polyethylene would be required to create 9 plastic bags?

33

An industrial detergent requires 19 \text{ mL} of water to be added to every 1 \text{ mL} of the detergent for safe usage. How many litres of water must be added to 610 \text{ mL} of detergent?

34

300 \text{ L} of rain falls over a 2100 \text{ m}^{2} field. Approximately how much rain falls over one half of the field in litres?

35

Luke is a locksmith. On weekends, if he is on call, he gets paid \$64.50 per hour plus a flat rate call out fee of \$75.

On Saturday he has 3 jobs that will take 1.5, 0.25 and 1.25 hours respectively to complete. How much will he earn on Saturday?

36

Tom is attending to a patient on the way to the emergency department. In the ambulance, he takes a quick measurement of the patient's heart rate, and finds it to be 36 beats per 20 seconds. An hour later, in the hospital he takes a more detailed measurement and finds the patient's heart rate to be 240 beats per 120 seconds.

a

Calculate the heart rate in beats per minute (bpm) for the first reading.

b

Calculate the heart rate in beats per minute (bpm) for the second reading.

c

Did the patient's heart rate increase or decrease between these readings?

37

The Ocean Zone theme park on the Gold Coast had 3220 people enter, and was open for 14 hours on Wednesday. On Thursday, it had 2970 people enter, and was open for 9 hours. If there are more than 270 people entering the park per hour, then Ocean Zone adds extra staff at the gate.

a

State the rate per hour of visitors entering the park on Wednesday.

b

State the rate per hour of visitors entering the park on Thursday.

c

On which day did Ocean Zone need extra staff?

38

Peter runs daily and usually runs 19 \text{ km} in 75 minutes. The last time he ran the 21 \text{ km} Sydney half marathon, it took him 126 minutes.

a

Find his running rate in km/h during his daily run.

b

Find his running rate in km/h during the half marathon.

c

In which activity was he running faster on average?

39

Two shearers wanted to work out who was the faster shearer.

Jenny sheared 144 sheep over 6 days, and Sean sheared 115 sheep in 5 days.

a

Find Jenny's rate per day in shearing sheep.

b

If Jenny continued at this rate, how many would she be able to shear in 25 days?

c

Find Sean's rate per day in shearing sheep.

d

Who sheared sheep at a faster daily rate?

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