How to Solve Compound Measures: Speed, Density and Pressure (IGCSE)
Compound measures combine two quantities into one, and they are a core Edexcel IGCSE Maths skill. This page covers speed, density and pressure, plus rates and the unit conversions exams rely on, including metric to imperial. You will learn to pick the right formula, rearrange it safely, and keep units consistent, with worked examples laid out one step per line and auto-marked practice below.
How to Solve Compound Measures Questions
A compound measure combines two quantities into one, such as speed (distance and time) or density (mass and volume). The method is the same for every type.
- Pick the formula: speed \(=\dfrac{\text{distance}}{\text{time}}\), density \(=\dfrac{\text{mass}}{\text{volume}}\), pressure \(=\dfrac{\text{force}}{\text{area}}\), or a rate \(=\dfrac{\text{amount}}{\text{time}}\).
- Rearrange it for the quantity you want (the formula triangle below shows multiply or divide).
- Convert units first, before substituting: minutes to hours, cm to m, miles to km, and so on.
- Substitute and solve, one equals sign per line, and always write the correct unit in the answer.
Core ideas
The formula triangle: cover what you want
Put the top quantity on top and the other two underneath. Cover the one you need: two side by side means multiply; one over the other means divide.
Worked examples
💡 Example 1: speed
A train covers 84 km in 1 hour 12 minutes. Find its average speed in km/h.
Convert the time: \(1\text{ h }12\text{ min}=1.2\) h.
\[ \begin{array}{rcl} \text{speed} &=& \dfrac{\text{distance}}{\text{time}} \\ &=& \dfrac{84}{1.2} \\ &=& \mathbf{70}\ \text{km/h} \end{array} \]What's happening?
Convert minutes to hours first: \(12\text{ min}=0.2\) h. Then divide distance by time.
💡 Example 2: km/h to m/s
Write a speed of 90 km/h in m/s.
1 km \(=1000\) m and 1 h \(=3600\) s.
\[ \begin{array}{rcl} 90\ \text{km/h} &=& \dfrac{90\times 1000}{3600}\ \text{m/s} \\ &=& \mathbf{25}\ \text{m/s} \end{array} \]What's happening?
To go from km/h to m/s, multiply by 1000 and divide by 3600 (the same as dividing by 3.6).
💡 Example 3: density (find the mass)
Oak has a density of 0.7 g/cm³. Find the mass of a 300 cm³ block of oak.
What's happening?
Cover \(M\) in the triangle: it sits over \(\rho\) and \(V\) side by side, so multiply.
💡 Example 4: pressure
A crate pushes down with a force of 720 N on a base of area 0.3 m². Find the pressure in N/m².
What's happening?
Pressure is force divided by area. \(2400\) N/m² is the same as \(2400\) Pa.
💡 Example 5: rate of flow
A tap fills a 240 litre tank in 16 minutes. Find the flow rate in litres per minute.
What's happening?
A rate is an amount per unit of time. Divide the total litres by the total minutes.
💡 Example 6: miles to km (speed)
A car travels at 50 miles per hour. Using 5 miles = 8 km, find the speed in km/h.
So the speed is \(\mathbf{80}\) km/h.
What's happening?
Convert the imperial unit to metric using \(5\text{ miles}=8\text{ km}\): multiply by \(\tfrac{8}{5}\).
🔑 Key points
- Speed \(=\dfrac{\text{distance}}{\text{time}}\), density \(=\dfrac{\text{mass}}{\text{volume}}\), pressure \(=\dfrac{\text{force}}{\text{area}}\), rate \(=\dfrac{\text{amount}}{\text{time}}\).
- Use the formula triangle: side by side means multiply, one over the other means divide.
- Convert units before substituting, and write the unit in every answer.
- \(1\,\text{g/cm}^3 = 1000\,\text{kg/m}^3\); km/h \(\div\,3.6\) gives m/s; \(1\,\text{Pa}=1\,\text{N/m}^2\).
- Imperial to metric: \(5\text{ miles}=8\text{ km}\), \(1\text{ m}\approx 3.28\text{ feet}\).
⚠️ Common pitfalls
- Mixing units: using minutes where the answer needs hours, or cm where it needs m.
- Forgetting to convert before substituting into the formula.
- Dividing the wrong way: density is \(\dfrac{m}{V}\), not \(\dfrac{V}{m}\).
- Using a length (like a diameter) where the formula needs an area for pressure.
- Writing a bare number with no unit: an exam answer needs km/h, g/cm³, N/m², and so on.