0580
Compound Measures
Number
Rates in everyday contexts
- The same structure covers a wide range of contexts named by the specification
| Rate | Calculated as |
|---|---|
| Hourly pay | total pay ÷ hours worked |
| Exchange rate | amount in one currency ÷ amount in the other |
| Flow rate | volume ÷ time |
| Fuel consumption | fuel used ÷ distance travelled |
| Population density | population ÷ area |
- Each is handled by dividing, then attaching units built from the two quantities
- A tank taking 25 minutes to receive 4500 litres has a flow rate of 180 litres per minute
- A region of 800 km² holding 2.4 million people has a population density of 3000 people per km²
Exam tip
Speed, distance and time must be known; density and pressure are normally printed in the question itself. Convert part-hours properly — 3 hours 45 minutes is 3.75 hours, never 3.45 — and for a journey in stages divide the total distance by the total time rather than averaging the separate speeds. The units are often worth a mark on their own.
Worked example
An average speed with a part-hour
A train travels 285 km in 3 hours 45 minutes. Work out its average speed in km/h.
Solution:
- The answer is wanted in km/h, so the time must be in hours
- 45 minutes is 45 ÷ 60 = 0.75 hours
- The journey takes 3.75 hours, not 3.45
- Speed = distance ÷ time = 285 ÷ 3.75
- Average speed = 76 km/h
- Check by reversing: 76 × 3.75 = 285