Rates and compound units | Year 11

01 / LEARN

The idea, step by step

Understand the idea

A rate compares unlike quantities: kilometres per hour, litres per second or dollars per square metre. The word per indicates division. Multiplying by a compatible amount cancels the denominator unit.

A compound conversion may change both units. To change m/s to km/h, combine 0.001 kilometres per metre with 3600 seconds per hour; the overall factor is 3.6.

Choose and apply a method

Decide what is being sought before substituting. At constant speed, distance equals speed times time. At a fixed unit price, cost equals price per unit times quantity. Convert time to the denominator unit before multiplying.

State any constant-rate assumption. Density is mass per volume, while paint coverage may be area per litre. Identify which way around a quoted rate is written: inverting a rate changes multiplication into division.

d = v t, mass = density \times volume

A common trap

Multiplying km/h by a time in minutes without converting.

Instead: Write the time in hours first, or convert the rate to kilometres per minute.

02 / WORKED EXAMPLES

See the thinking

Example 1

Convert speed

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

In one hour the runner travels $5 \times 3600 = 18 000$ m.
This is 18 km in one hour.

18 km/h.

Example 2

Use flow rate

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

0.3 m $3 = 300$ L.
Time $= 300 / 12 = 25$ minutes.

25 minutes.

Check your understanding

Convert 72 km/h to m/s.

Show answer

20 m/s.

$72 / 3.6 = 20$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF 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
$45 / 9 = 5$ 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 ↗

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