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3.025 Convert rates

Worksheet
Convert rates
1

The admission for a concert starts at 6 pm and closes at 7 pm. There are 900 people attending and they arrive at a constant rate.

a

How many minutes will the concert last?

b

Find the flow of people per minute.

2

A cyclist travels 70 \text{ m} every 10 seconds.

a

How many lots of 10 seconds are in 1 minute?

b

Hence find the speed of the cyclist in metres per minute.

c

How many metres will the cyclist travel in one hour?

d

Hence find the speed of the cyclist in kilometres per hour.

3

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

a

How many lots of 20 \text{ cm} are there in 1 \text{ m}?

b

How long does it take for the worm to travel 1 \text{ m}?

c

Hence, state the rate of the worm's time taken per distance travelled in \text{sec/m}.

4

If 9600 \text{ L} of water flows through a tap in 8 hours, calculate the tap's flow rate per minute.

5

Convert the following as indicated:

a

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

b

300 \text{ mL/hr} to \text{mL/min}

c

36 \text{ dollars/hr} to \text{dollars/min}

d

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

e

36 \degree \text{/s} to \degree \text{/min}

f

21 \text{ m/min} to \text{m/s}

6

A bike travels 83 \text{ m} in 12 seconds.

a

How many lots of 12 seconds are there in 1 minute?

b

Find the speed of the bike in \text{m/min}.

7

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.

8

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}

9

Peter runs daily and usually covers his 19 \text{ km} in 75 \text{ min}. He also enters half marathon and full marathon events. The last time he ran the Sydney half marathon it took him 126 \text{ min} to complete the 21 \text{ km} event.

a

State his running rate during his daily run in \text{km/h}.

b

State his running rate during the half marathon in \text{km/h}.

c

In which event was he running faster on average? On his daily run or in the half marathon?

10

A runner approximates the distance between two street lights to be 33 \text{ m}. It takes him 10 \text{ sec} to run from one street light to the other.

State the runner's speed in:

a

\text{m/sec}

b

\text{m/min}

c

\text{m/h}

d

\text{km/h}

11

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}

12

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

13

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}

14

Order these trips in ascending order of average speed:

  • A Driving 180 \text{ km} in 3 hours

  • B Bicycling 132 \text{ km} in 4 hours

  • C A taxi trip that took 15 minutes to travel 11 \text{ km}

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Outcomes

ACMEM015

convert units of rates occurring in practical situations to solve problems

ACMEM016

use rates to make comparisons; for example, using unit prices to compare best buys, comparing heart rates after exercise

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