GCSE Maths revision · Ratio and proportion

Speed, density and pressure

Foundation and Higher

The idea

Compound measures combine two units: speed $= \frac{\text{distance}}{\text{time}}$ , density $= \frac{\text{mass}}{\text{volume}}$ , pressure $= \frac{\text{force}}{\text{area}}$ .

Write the formula and rearrange it for what you need.
Make the units match before you substitute.
For the best buy, compare the price per gram (or grams per penny).

Watch out $1$ hour $30$ minutes is $1.5$ hours, not $1.3$ .

See it worked

Worked exampleNon-calculator3 marks

A cyclist travels 18 km in 45 minutes. Work out the average speed in km/h.

$45/60$
$18/0.75$
45 minutes is 45/60 = 0.75 hours.
Average speed = distance $\div$ time = 18 $\div$ 0.75 = 24 km/h.

Answer $24\,\mathrm{km/h}$

Your turn

Question 1Calculator allowed4 marks

You may use a calculator.

(a) A train travels 150 km in 2 hours 30 minutes. Work out its average speed in km/h.

(b) A cyclist rides at 24 km/h for 45 minutes. How far does she travel?

Question 2Calculator allowed3 marks

An employee earns £16 per hour for the first 35 hours in a week and 1.5 times that rate for any further hours. Work out the pay for a 42-hour week.

Question 3Non-calculator3 marks

A journey consists of two equal distances. The speeds on the two sections are v km/h and (v + 20) km/h, where v > 0. The average speed for the complete journey is 48 km/h. Find v. You must show your working.

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