Speed, distance and time | Year 8

01 / LEARN

Understand the idea.

Three linked quantities

Average speed is total distance divided by elapsed time. With distance $d$ in kilometres and time $t$ in hours, $v = \frac{d}{t}$ has units km/h. The same relationship gives $d = v t$ and, for a nonzero speed, $t = \frac{d}{v}$ .

Choose compatible units before calculating. A speed in km/h requires time in hours, so $45$ minutes is $\frac{45}{60} = 0.75$ hour. The digits after a decimal point are hundredths, not minutes; $0.45$ hour is only $27$ minutes.

\begin{aligned} v & = \frac{d}{t} \\ d & = v t \\ t & = \frac{d}{v} \end{aligned}

A journey can have changing speed

For several journey stages, add the distances and add the elapsed times before dividing. A stop adds time but no distance. Include it when the question asks about the whole journey rather than only the moving time.

An ordinary mean of stage speeds works for equal durations. Otherwise the stages contribute different amounts of time and must be weighted accordingly. Total distance divided by total time handles both cases and does not assume a constant speed.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Average speed

A car travels 150 km in 2.5 hours. Find its average speed.

Worked solution

1
Select the average-speed relationship.
$v = \frac{d}{t}$
Average speed measures the distance covered per unit of elapsed time.
2
Substitute the compatible measurements.
$v = \frac{150}{2.5} = 60 km/h$
The distance is in kilometres and the time is already in hours.
3
Check the distance recovered.
$60 \times 2.5 = 150 km$
The calculated average speed over the given time produces the stated distance.

Answer

60 km/h.

EXAMPLE 02

Find the time

A journey is 54 km at a constant 72 km/h. How many minutes does it take?

Worked solution

1
Divide distance by speed to find hours.
$t = \frac{54}{72} = \frac{3}{4} h$
At 72 km/h, each hour accounts for 72 km of this constant-speed journey.
2
Convert the duration to minutes.
$\frac{3}{4} \times 60 = 45 min$
There are sixty minutes in one hour.
3
Check the distance using that duration.
$72 \times \frac{45}{60} = 54 km$
Forty-five minutes at the stated speed covers the required 54 km.

Answer

45 minutes.

03 / YOUR TURN

Try it yourself.

Check your understanding

How far do you travel at 80 km/h for 15 minutes?

Show answer & reasoning

20 km.

Convert time first: $15$ minutes is $\frac{15}{60} = \frac{1}{4}$ hour. Then $d = v t = 80 \times \frac{1}{4} = 20$ km.

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Find the average speed for 180 km in 3 hours.
1 mark
Find the average speed for 84 km in 1.2 hours.
2 marks
Find the distance travelled at 54 km/h for 2 hours.
1 mark
A bus travels at 90 km/h for 40 minutes. Find the distance.
2 marks
A runner covers 2.4 km in 15 minutes. Find the average speed in km/h.
2 marks
A car travels 60 km at 60 km/h, then 60 km at 30 km/h. Find its average speed over both stages.
3 marks

Read the worked solutions

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

Find the average speed for 180 km in 3 hours.
1 mark
$180 \div 3 = 60$ .
60 km/h.
Find the average speed for 84 km in 1.2 hours.
2 marks
$84 \div 1.2 = 70$ .
70 km/h.
Find the distance travelled at 54 km/h for 2 hours.
1 mark
$d = 54 \times 2 = 108$ .
108 km.
A bus travels at 90 km/h for 40 minutes. Find the distance.
2 marks
40 min is $\frac{2}{3}$ h.
$90 \times \frac{2}{3} = 60$ km.
60 km.
A runner covers 2.4 km in 15 minutes. Find the average speed in km/h.
2 marks
15 min is 0.25 h.
$2.4 \div 0.25 = 9.6$ .
9.6 km/h.
A car travels 60 km at 60 km/h, then 60 km at 30 km/h. Find its average speed over both stages.
3 marks
The times are $60 \div 60 = 1$ h and $60 \div 30 = 2$ h.
Total distance is 120 km and total time is 3 h.
$120 \div 3 = 40$ km/h.
40 km/h.

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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.

Three linked quantities

A journey can have changing speed

See the method in action.

Average speed

Select the average-speed relationship.

Substitute the compatible measurements.

Check the distance recovered.

Find the time

Divide distance by speed to find hours.

Convert the duration to minutes.

Check the distance using that duration.

Try it yourself.

Check your understanding

Keep practising