Rates and compound units | Year 11

01 / LEARN

Understand the idea.

Understand the idea

A rate compares quantities with different units. The word 'per' means division: litres per minute describes volume divided by time. Multiplying by a time in minutes then gives a volume because the minute units cancel.

A compound unit conversion may change both numerator and denominator. For speed, one hour contains 3600 seconds and one kilometre contains 1000 metres. Combining these relationships gives a factor of $\frac{3600}{1000} = 3.6$ from metres per second to kilometres per hour.

Choose and apply a method

Decide which quantity is unknown before choosing an operation. At constant speed, distance is speed times time; at constant flow, time is volume divided by flow rate. Match the time or volume unit to the quoted rate before calculating.

Check how the rate is written. Paint coverage in square metres per litre differs from litres per square metre, just as density is mass per volume rather than volume per mass. State any assumption that the quoted rate remains constant throughout the task.

\begin{aligned} d & = v t \\ mass & = density \times volume \end{aligned}

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Convert speed

A runner travels at 5 m/s. Express this in km/h.

Worked solution

1
Find the distance covered in one hour.
$d = 5 \times 3600 = 18 000 m$
There are 3600 seconds in an hour, with 5 metres travelled in each second.
2
Convert that distance to kilometres.
$18 000 \div 1000 = 18 km$
There are 1000 metres in one kilometre.
3
State the speed with its new time unit.
$v = 18 km/h$
Travelling 18 kilometres in one hour corresponds to 18 kilometres per hour.

Answer

18 km/h.

EXAMPLE 02

Use flow rate

Water flows at 12 L/min. How long to supply 0.3 m $3$ at this constant rate?

Worked solution

1
Convert the required volume to litres.
$0.3 m^{3} = 300 L$
The flow rate is supplied in litres per minute.
2
Divide volume by the constant flow rate.
$t = \frac{300}{12} = 25 min$
Twelve litres arrive each minute, so the required time is the number of 12 litre portions.
3
Check the delivered volume.
$12 \times 25 = 300 L$
The computed time supplies exactly the required volume when the flow remains constant.

Answer

25 minutes.

03 / YOUR TURN

Try it yourself.

Check your understanding

Convert 72 km/h to m/s.

Show answer & reasoning

20 m/s.

Reverse the metres-per-second conversion by dividing by 3.6: $72 \div 3.6 = 20 m/s$ . Equivalently, $72 000$ metres divided by 3600 seconds gives the same result.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Convert 15 m/s to km/h.
2 marks
A vehicle travels at 80 km/h for 45 minutes at constant speed. Find distance.
2 marks
Carpet costs AUD 28 per square metre. Find the cost of 12.5 m $2$ .
2 marks
A pump delivers 2.5 L/s. Find volume delivered in 4 minutes.
2 marks
A material has density 7.8 g/cm $3$ and volume 20 cm $3$ . Find mass.
2 marks
Paint covers 9 m $2$ per litre. How much paint covers 45 m $2$ ?
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Convert 15 m/s to km/h.
2 marks
$15 \times 3.6 = 54$ .
54 km/h.
A vehicle travels at 80 km/h for 45 minutes at constant speed. Find distance.
2 marks
45 minutes is 0.75 h.
$80 \times 0.75 = 60$ km.
60 km.
Carpet costs AUD 28 per square metre. Find the cost of 12.5 m $2$ .
2 marks
$28 \times 12.5 = 350$ .
AUD 350.
A pump delivers 2.5 L/s. Find volume delivered in 4 minutes.
2 marks
4 minutes is 240 s.
$2.5 \times 240 = 600$ L.
600 L.
A material has density 7.8 g/cm $3$ and volume 20 cm $3$ . Find mass.
2 marks
$7.8 \times 20 = 156$ g.
156 g.
Paint covers 9 m $2$ per litre. How much paint covers 45 m $2$ ?
2 marks
$\frac{45}{9} = 5$ L; divide area by the area-per-litre rate.
5 L.

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Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

In this lesson

Understand the idea.

Understand the idea

Choose and apply a method

See the method in action.

Convert speed

Find the distance covered in one hour.

Convert that distance to kilometres.

State the speed with its new time unit.

Use flow rate

Convert the required volume to litres.

Divide volume by the constant flow rate.

Check the delivered volume.

Try it yourself.

Check your understanding

Keep practising