R1, R11Ratio, Proportion & Rates of ChangeFoundation & HigherGrades 3–6

Compound Measures

Q: How do I convert a decimal time like 2.7 hours to hours and minutes?

Keep the 2 hours and multiply the decimal part by 60: 0.7 60 = 42, so 2 hours 42 minutes.

A compound measure combines two different units: speed in kilometres per hour, density in grams per cubic centimetre, pressure in newtons per square metre. Each is a rate — one quantity divided by another — and its unit tells you the formula. "Per" means "divide by".

40 min Video by Maths Genie AQA GCSE Maths

The big picture

You do not need to memorise three separate formula triangles. The unit gives it away: km/h is kilometres ÷ hours, so speed = distance ÷ time. Rearranging gives the other two versions.

Most lost marks come from units, not formulas. Minutes must become hours before using km/h, and 45 minutes is 0.75 hours, not 0.45. Converting compound units — such as km/h to m/s — needs both parts converted.

Speed and DensityCurated by Kepler, not produced by us. Watch it, then read the notes below.

Open on YouTube

What you'll learn

Use speed = distance ÷ time and its rearrangements
Use density = mass ÷ volume and pressure = force ÷ area
Convert between time units and between compound units
Solve problems involving other rates, such as flow rate

Speed, distance and time

Speed $= \frac{distance}{time}$ , so distance $=$ speed $\times$ time and time $= \frac{distance}{speed}$ .

Convert minutes to hours by dividing by 60: 20 minutes $= \frac{20}{60} = \frac{1}{3}$ hour, and 1 hour 24 minutes $= 1.4$ hours. Average speed uses the total distance and the total time.

11 hour 15 minutes

= 1.25

hours.

2Speed

= 150 \div 1.25 = 120

Answer

120

km/h

Your turnSame method, new numbers — try it before moving on.

A cyclist rides at 18 km/h for 40 minutes. How far do they travel, in km?

Your answer

Your turnSame method, new numbers — try it before moving on.

A runner covers 3 km in 15 minutes, then 2 km in 15 minutes. What is the average speed in km/h?

Your answer

Tip — Average speed is not the average of the two speeds: $\frac{60 + 100}{2} = 80$ , but Sara's true average is 70 km/h, because she spent longer at the slower speed.

Density and pressure

Density $= \frac{mass}{volume}$ , measured in g/cm³ or kg/m³.

Pressure $= \frac{force}{area}$ , measured in N/m² (also called pascals). The same force over a smaller area gives a greater pressure — which is why a knife cuts and snowshoes do not sink.

Cover the quantity you want: the others show whether to multiply (side by side) or divide (one above the other).

1Mass

=

density

\times

volume.

19.3 \times 40 = 772

Answer

772

Your turnSame method, new numbers — try it before moving on.

A block of wood has mass 540 g and volume 900 cm³. Find its density in g/cm³.

Your answer

Your turnSame method, new numbers — try it before moving on.

A force of 240 N produces a pressure of 80 N/m². What is the area, in m²?

Your answer

Converting compound units

Convert each part separately. To change km/h to m/s, change kilometres to metres ( $\times 1000$ ) and hours to seconds ( $\div 3600$ ).

Area and volume units convert with squared and cubed factors: $1$ m² $= 10, 000$ cm² and $1$ m³ $= 1, 000, 000$ cm³.

172 km/h

= 72, 000

m in 3600 s.

72, 000 \div 3600 = 20

Answer

20

m/s

Your turnSame method, new numbers — try it before moving on.

Convert 15 m/s to km/h.

Your answer

Where 3.6 comes from

Multiplying by 3.6 converts m/s to km/h, because $\frac{3600}{1000} = 3.6$ . It is a useful shortcut, but deriving it from the separate conversions is what earns method marks.

Other rates

Any "per" quantity works the same way: litres per minute, pounds per hour, words per minute. Identify what is divided by what, and keep track of units.

1Time

= 1350 \div 45 = 30

minutes.

Answer30 minutes

Your turnSame method, new numbers — try it before moving on.

A printer prints 24 pages per minute. How many minutes does it take to print 1,080 pages?

Your answer

Think like an examiner

State units in the final answer — they are often required for the accuracy mark.
Show time conversions explicitly: "1 h 15 min = 1.25 h".
In multi-step problems (e.g. combining two materials), write what each number represents.

Compound measures

speed = \frac{distance}{time}

km/h, m/s.

density = \frac{mass}{volume}

g/cm³, kg/m³.

pressure = \frac{force}{area}

N/m².

Watch out for these

2 hours 30 minutes

= 2.3

hours.

30 minutes is half an hour:

2.5

hours.

Average speed as the mean of two speeds.

Total distance ÷ total time.

Converting km/h to m/s by dividing by 60.

Multiply by 1000 and divide by 3600.

Using an area in cm² with a force in N to get N/m².

Convert the area to m² first.

Stretch yourself

200 cm³ of metal A (density 8 g/cm³) is melted and mixed with 300 cm³ of metal B (density 5 g/cm³). Find the density of the resulting alloy, assuming no change in total volume.

Hint — Densities do not simply average. Find the total mass and the total volume.

Questions students ask

Do I need to learn the formulas?

Yes — speed, density and pressure formulas are not given on the exam. The units remind you: g/cm³ means grams divided by cubic centimetres.

How do I convert a decimal time like 2.7 hours to hours and minutes?

Keep the 2 hours and multiply the decimal part by 60:

0.7 \times 60 = 42

, so 2 hours 42 minutes.

What is the difference between speed and velocity?

At GCSE Maths they are treated the same. In physics, velocity also includes direction.

Key takeaways

"Per" means divide: the unit shows the formula.
Speed = distance ÷ time; density = mass ÷ volume; pressure = force ÷ area.
Convert minutes to hours by dividing by 60.
Average speed = total distance ÷ total time.
Convert compound units one part at a time.

Exam-style questions

Practise it the way it is examined

3 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.

Question 1Grade 32 marks

A car travels 204 km at an average speed of 68 km/h. How long does the journey take?[2]

Question 2Grade 53 marks

A cylinder of copper has radius 2 cm and height 10 cm. The density of copper is 8.96 g/cm³.

Work out the mass of the cylinder. Give your answer to 3 significant figures.[3]

Question 3Grade 62 marks

A cheetah can run at 30 m/s. A racing car travels at 100 km/h.

Which is faster? Show how you decide.[2]

Unlimited practice

Skill drill

A new question every time, marked instantly, with a full worked solution. Aim for a streak of five, then move up a level.

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Real past-paper questions on Compound Measures, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.

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Compound Measures

Speed, distance and time

Density and pressure

Converting compound units

Other rates

Practise it the way it is examined

Skill drill

Practise this topic

Related topics

Compound Measures

Speed, distance and time

Density and pressure

Converting compound units

Other rates

Practise it the way it is examined

Skill drill

Practise this topic

Related topics