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11.06 Convert rates

Worksheet
Rates
1

An athlete runs 270\text{ m} in 27 seconds. What is his speed in \text{ km/hr}?

2

In an ice cream eating contest, the winner ate 2.22 litres of ice cream in 2 minutes.

What was the winner's rate of consumption of ice-cream in \text{ mL/s}?

3

Which two of the following rates are equivalent?

  • Rate A: Writing 34 words per second

  • Rate B: Writing 68 words in 30 seconds

  • Rate C: Writing 714 words in 21 minutes

  • Rate D: Writing 816 words per hour

  • Rate E: Writing 34 words per minute

4

Convert 80 \text{ m/s} to \text{km/hr} by solving the following:

a

Convert 80 \text{ m/s} to \text{km/s}.

b

Convert from \text{km/s} to \text{km/hr}.

5

Convert:

a

468\text{ km/hr } into \text{m/s}

b

170\text{ m/min} into \text{km/hr}

c

40\text{ mm/s} into \text{cm/min}

d

9\text{ cents/g} into \$\text{/kg}

e

10\text{ mL/min} into \text{L/day}

f

410\text{ g/s} into \text{t/hr}

g

300 \text{ mL/h} into \text{ mL/min}

h

600 \text{ km/hr} into \text{km/min}

i

\$36 \text{/hr} into \$ \text{/min}

j

96 \text{ L/day} into \text{L/h}

k

36 \degree \text{/s} into \text{degrees/min}

Applications
6

A worm takes 15 seconds to travel 20\text{ cm}.

a

How long does it take for the worm to travel 1 metre?

b

Find the rate of the worm's time spent per metre distance traveled.

7

A cyclist travels 70 \text{ m} per 10 seconds. Find the speed of the cyclist in metres per minute.

8

If 9600 \text{ L} of water flow through a tap in 8 hours, what is the tap's flow rate per minute?

9

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

10

Mae ran for 4 hours at the speed of 4 \text{ km/h}.

a

Express Mae's speed in \text{m/h}.

b

Hence, state the total distance Mae travelled in metres.

11

A crabeater seal can filter 0.9 \text{ L} of water in each dive while looking for food during a 30-minute time period. State the rate of water filtered in:

a

\text{L/min}

b

\text{L/h}

c

\text{mL/min}

d

\text{mL/s}

12

A runner approximates the distance between two street lights to be 33 \text{ m}. It takes him 10 seconds to run from one street light to the other. State the runner's speed in:

a

\text{m/s}

b

\text{m/min}

c

\text{m/h}

d

\text{km/h}

13

A cyclist approximates the distance between two trees as 39 \text{ m}. She counts 30 heart beats as she cycles from one tree to the other. The cyclist's smart watch says that her heart is beating at 90 \text{ bpm}.

a

How many seconds does it take the cyclist to get from one tree to the other?

b

State the cyclist's speed in:

i

\text{m/s}

ii

\text{m/min}

iii

\text{m/h}

iv

\text{km/h}

14

A baby is weighed on their first birthday and found that they've gained 5.475 \text{ kg} since they were born. Assuming there are 365 days in a year, state the rate of growth, correct to three decimal places in:

a

Kilograms/day

b

Grams/day

c

Grams/hour

15

The Earth completes one full rotation in a day. As it rotates, a particular point on the Earth moves 18\,900 \text{ km} in 12 hours. State the speed of the point on the Earth in:

a

Kilometres/day

b

\text{km/h}

c

\text{m/h}

d

\text{m/s}

16

Maria ran for 4 hours at the speed of 10\text{ km/h} .

a

Express her speed in metres per hour.

b

Hence, what was the total distance Maria travelled in metres?

17

A car is travelling at 26\text{ m/s}. How many kilometres does it travel in 1 hour?

18

A car travels 520.2\text{ km} in 10 hours and 12 minutes. Calculate the car's average speed for the trip.

19

Michael is driving his car. He knows how far he has travelled in kilometres, and how long it has taken him in minutes. Determine whether the following rates can be used to calculate his average speed:

a

kilometres/hour

b

kilometres/minute

c

hours/minute

20

A child is weighed on their first birthday to find that they have gained 9.855 kilograms since they were born.

a

What is the rate of growth in kilograms per day?

b

What is the rate of growth in kilograms per hour?

c

What is the rate of growth in grams per hour?

21

Marie cycles 77 kilometres in 7 hours on her bike. Determine whether the following journeys would have an equivalent speed to Marie's.

a

79 kilometres in 9 hours.

b

154 kilometres in 14 hours.

c

7 kilometres in 77 hours.

d

38.5 kilometres in 14 hours.

22

A crabeater seal can filter 0.975 litres of water in each dive looking for food. They can stay under water for 39 minutes each dive.

a

Find the rate of water filtered in \text{L/min}.

b

Find the rate of water filtered in \text{mL/min}.

c

Find the rate of water filtered \text{mL/s}. Round your answer to two decimal places.

23

The earth’s surface receives energy from the sun at a rate of 1.296 \text{ kW/m} ^2. Consider that1000\text{ J/sec}= 1\text{ kW} and 1055\text{ J}= 1\text{ BTU} (British Thermal Unit):

a

Find this rate in joules per second per \text{cm}^2.

b

Find this rate in BTUs per hour per \text{cm}^2. Round your answer to two decimal places.

24

The speed limit on a particular road in the US is 70 miles per hour. An Australian visiting the country is more familiar with the speeds using the unit \text{km/h}.

a

What is the speed limit in kilometres per hour?

b

If a car is travelling at 35 metres/second, by how many kilometres per hour is the car exceeding the speed limit?

25

Kilimanjaro, the tallest mountain in Africa, is 20\,322\text{ ft} high. Note that 1\text{ ft}= 0.3048\text{ m}.

a

What is its height in metres? Do not round your answer.

b

A group of mountain climbers set a challenge to tackle the Seven Summits, the tallest mountains in each continent, starting with Kilimanjaro. If it takes this party of climbers 4 days, 12 hours and 30 minutes to climb to the peak, what is the average rate of ascent in metres per hour? Round your answer to one decimal place.

26

Patricia eats 7.2 litres of ice cream in 6 minutes in an ice-cream eating contest. Find Patricia's rate of ice-cream consumption in millilitres per second.

27

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

28

Tectonic plates are large segments of the earth’s crust that move slowly. The image below shows the 15 major plates in the world:

Suppose that the Carribean plate moves 4.8\text{ cm} per year.

a

Assuming a non-leap year, how far does it move in 1 second?

b

What is the speed of the movement of the plate in \text{km/million} years?

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Outcomes

2.3.8

review identifying common usage of rates, such as km/h

2.3.9

convert units for rate; for example, km/h to m/s, mL/min to L/h

2.3.11

use rates to make comparisons

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