Speed, distance and time | Year 8

01 / LEARN

The idea, step by step

Three linked quantities

Average speed compares total distance travelled with total time taken. With kilometres and hours, the result is km/h. The relationship can also find distance or time. Choose a matching set of units before substituting numbers.

Convert minutes to a fraction of an hour: 30 min is $1 / 2$ h and 45 min is $3 / 4$ h. Writing 45 min as 0.45 h changes the actual duration.

v = \frac{d}{t}, d = v t, t = \frac{d}{v}

A journey can have changing speed

Average speed does not say that a traveller moved at that speed every moment. For a trip with stages, add the stage distances and stage times, then divide the totals. Include stops if the question asks for the whole journey.

Taking the ordinary average of two speeds is generally wrong when the time spent at each speed differs. Using total distance and total time works for every such journey.

A common trap

The average of two stage speeds always gives the journey average.

Instead: Only equal time intervals justify an ordinary mean of the two speeds. Otherwise find total distance divided by total time.

02 / WORKED EXAMPLES

See the thinking

Example 1

Average speed

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

Use $v = d / t$ .
Calculate $150 \div 2.5 = 60$ .
Check: $60 \times 2.5 = 150$ km.

60 km/h.

Example 2

Find the time

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

$t = 54 \div 72 = 0.75$ hours.
Convert to minutes: $0.75 \times 60 = 45$ .
The unit change is essential: 0.75 is hours, not minutes.

45 minutes.

Check your understanding

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

Show answer

20 km.

15 minutes is $1 / 4$ hour; $80 \times 1 / 4 = 20$ .

03 / WORKSHEET

Your turn

6 questions · 11 marks · Work at your own pace.

Worksheet PDF 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 $2 / 3$ h.
$90 \times 2 / 3 = 60$ 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 ↗

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