YEAR 8 · RATIOS AND RATES · 15 MIN

Converting compatible units

Convert a rate by changing both the quantity unit and the time unit correctly.

In this lesson

Convert between km/h and m/s
Convert capacity and mass rates
Check a conversion by reversing it

Before you start

Metric unit conversion
Speed, distance and time

01 / LEARN

Understand the idea.

A rate contains two units

A rate contains two units, and either can change. The rate $72 km/h$ means $72$ kilometres in one hour. Replace these with the equivalent distance and time, $72.000$ metres in $3.600$ seconds, before finding metres per second.

Changing only kilometres to metres gives metres per hour, not metres per second. Keep the quantity labels visible through the conversion so you can see whether both the numerator unit and the denominator unit now match the target.

Useful conversion checks

Since $1 m/s = 3.6 km/h$ , multiply m/s by $3.6$ to obtain km/h and divide km/h by $3.6$ to obtain m/s. This factor follows from the metric distance conversion and the sixty-by-sixty time conversion.

Ask how many of the old units fit in the new unit. A kilogram contains ten groups of $100$ g, so a price per kilogram is ten times the price per $100$ g. Reversing the conversion should restore the original rate.

1 m/s = 3.6 km/h

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Kilometres per hour to metres per second

Convert 72 km/h to m/s.

Worked solution

1
Convert the distance and time separately.
$\begin{aligned} 72 km & = 72.000 m \\ 1 h & = 3.600 s \end{aligned}$
Equivalent distance and time measurements preserve the speed.
2
Find the distance per second.
$\frac{72.000 m}{3.600 s} = 20 m/s$
Dividing by the number of seconds gives the distance for one second.
3
Reverse the conversion as a check.
$20 \times 3.6 = 72 km/h$
The converted rate represents the same motion as the starting rate.

Answer

20 m/s.

EXAMPLE 02

Metres per minute to metres per second

Convert 450 m/min to m/s.

Worked solution

1
Rewrite one minute in seconds.
$1 min = 60 s$
The distance unit is already metres, so only the time unit needs changing.
2
Divide the minute distance among sixty seconds.
$\frac{450 m}{60 s} = 7.5 m/s$
The rate must state the distance per one second rather than per minute.
3
Check the distance in one minute.
$7.5 \times 60 = 450 m$
Sixty seconds at the converted rate recovers the original minute distance.

Answer

7.5 m/s.

03 / YOUR TURN

Try it yourself.

Check your understanding

Convert 10 m/s to km/h.

Show answer & reasoning

36 km/h.

In one hour, $10 m/s$ covers $10 \times 3.600 = 36.000$ m. This is $36$ km, so the equivalent speed is $36 km/h$ .

Keep practising

6 worksheet questions · 14 marks

Open worksheet Worked solutions

Read the questions online

Convert 36 km/h to m/s.
2 marks
Convert 15 m/s to km/h.
2 marks
Convert 3.5 L/min to mL/min.
2 marks
Convert 240 cm/min to m/s.
3 marks
A food costs AUD 0.80 per 100 g. Find its cost per kilogram.
2 marks
A runner covers 2.7 km in 15 minutes. Find the average speed in m/s.
3 marks

Read the worked solutions

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

Convert 36 km/h to m/s.
2 marks
$36 \div 3.6 = 10$ .
10 m/s.
Convert 15 m/s to km/h.
2 marks
$15 \times 3.6 = 54$ .
54 km/h.
Convert 3.5 L/min to mL/min.
2 marks
Each litre is 1,000 mL.
$3.5 \times 1000 = 3500$ .
3,500 mL/min.
Convert 240 cm/min to m/s.
3 marks
240 cm is 2.4 m.
$2.4 \div 60 = 0.04$ m/s.
0.04 m/s.
A food costs AUD 0.80 per 100 g. Find its cost per kilogram.
2 marks
1 kg contains ten lots of 100 g.
$0.80 \times 10 = 8$ .
AUD 8/kg.
A runner covers 2.7 km in 15 minutes. Find the average speed in m/s.
3 marks
2.7 km is 2,700 m; 15 min is 900 s.
$2700 \div 900 = 3$ .
3 m/s.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Ratio scaling and division review; unit rates; comparing rates and best buys; speed, distance and time; converting compatible units; direct-proportion tables and graphs; modelling practical rate problems and checking assumptions.

Official curriculum source ↗

In this lesson

Understand the idea.

A rate contains two units

Useful conversion checks

See the method in action.

Kilometres per hour to metres per second

Convert the distance and time separately.

Find the distance per second.

Reverse the conversion as a check.

Metres per minute to metres per second

Rewrite one minute in seconds.

Divide the minute distance among sixty seconds.

Check the distance in one minute.

Try it yourself.

Check your understanding

Keep practising