Rates and unit conversions | Year 9

01 / LEARN

The idea, step by step

A rate has two units

A rate compares quantities measured in different units, such as dollars per kilogram, kilometres per hour or litres per minute. To compare rates fairly, express both in the same units.

Convert the numerator and denominator separately. One kilometre is 1,000 metres and one hour is 3,600 seconds, so $1 km/h = 1000 / 3600 m/s$ . This gives division by 3.6 from km/h to m/s.

speed = \frac{distance}{time}

Use consistent time and distance

At constant speed, $d = v t$ , $v = d / t$ and $t = d / v$ . Match the units before substituting: a speed in km/h needs a time in hours for distance in kilometres.

For average speed, divide the total distance by the total time. Do not take an unweighted average of two speeds unless the travel times are equal. Include stops if the question asks for the average over the whole journey.

A common trap

Convert km/h to m/s by multiplying by 3.6.

Instead: One hour contains many seconds, so the numeric speed becomes smaller. Divide km/h by 3.6; multiply m/s by 3.6.

02 / WORKED EXAMPLES

See the thinking

Example 1

Convert a speed

Convert 72 km/h to metres per second.

Convert kilometres to metres and hours to seconds: $72 \times 1000 / 3600$ .
Simplify to $72 \div 3.6 = 20$ .

20 m/s

Example 2

Time in a rate problem

A pump transfers 135 L in 7.5 min at a constant rate. How long for 216 L?

The rate is $135 \div 7.5 = 18$ L/min.
Time is $216 \div 18 = 12$ min.

12 minutes

Check your understanding

A cyclist travels at 15 km/h for 24 minutes. How far does the cyclist travel?

Show answer

6 km

$24 / 60 = 0.4$ h, so $d = 15 \times 0.4 = 6$ km.

03 / WORKSHEET

Your turn

6 questions · 13 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Convert 54 km/h to m/s.
2 marks
Convert 8 m/s to km/h.
2 marks
A car travels 126 km in 1.5 h. Find its average speed.
2 marks
A tap fills 42 L in 3.5 min. Find its rate in L/min.
2 marks
Which is cheaper: 750 g of cereal for 4.50 dollars, or 1.2 kg for 6.60 dollars?
3 marks
A bus travels 40 km in 50 minutes, then stops for 10 minutes. Find the average speed for the entire hour.
2 marks

Read the worked solutions

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

Convert 54 km/h to m/s.
2 marks
$54 \div 3.6 = 15$ .
15 m/s
Convert 8 m/s to km/h.
2 marks
$8 \times 3.6 = 28.8$ .
28.8 km/h
A car travels 126 km in 1.5 h. Find its average speed.
2 marks
$v = 126 \div 1.5 = 84$ km/h.
84 km/h
A tap fills 42 L in 3.5 min. Find its rate in L/min.
2 marks
$42 \div 3.5 = 12$ L/min.
12 L/min
Which is cheaper: 750 g of cereal for 4.50 dollars, or 1.2 kg for 6.60 dollars?
3 marks
$750$ g $= 0.75$ kg.
First rate: $4.50 / 0.75 = 6.00$ dollars/kg.
Second rate: $6.60 / 1.2 = 5.50$ dollars/kg.
The 1.2 kg pack.
A bus travels 40 km in 50 minutes, then stops for 10 minutes. Find the average speed for the entire hour.
2 marks
Total time is $50 + 10 = 60$ min $= 1$ h.
Average speed $= 40 / 1 = 40$ km/h.
40 km/h

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 9 proportional modelling, rates, scale, similarity and enlargement. Assumptions, interpretation and model limitations are taught alongside calculation.

Official curriculum source ↗

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