Speed, distance and time, and compound measures
A compound measure combines two quantities, such as kilometres per hour or grams per cm³. Speed, density and pressure all follow the same pattern: one formula you can rearrange three ways, and units that must match.
Part 1 of 3: Learn it
In short
- Speed is distance ÷ time, density is mass ÷ volume and pressure is force ÷ area.
- Convert minutes to hours by dividing by 60: 20 minutes = 1/3 hour, not 0.2 hours.
- Average speed = total distance ÷ total time.
Where this is in your specification
Spec points: DfE R1 and R11
| Board | Topic: Rates, compound measures and growth |
|---|---|
| DfE content | R1, R11, R14, R15, R16 |
| AQA 8300 | Ratio, proportion and rates of change |
| Edexcel 1MA1 | Ratio, proportion and rates of change |
| OCR J560 | 5 Ratio, proportion and rates of change |
| Eduqas C300 | HR2, HR12, HR15 to HR17 |
| Cambridge IGCSE 0580 | E1.12, E1.15 to E1.17, E2.9 |
The formulas
| Measure | Formula | Typical units |
|---|---|---|
| Speed | distance ÷ time | m/s, km/h, mph |
| Density | mass ÷ volume | g/cm³, kg/m³ |
| Pressure | force ÷ area | N/m² (pascals), N/cm² |
Rearranged, distance is speed × time, and time is distance ÷ speed. The units of the answer come from the units you put in: kilometres and hours give km/h.
Time conversions
- Minutes to hours: divide by 60. 45 minutes = 0.75 hours.
- Decimal hours to minutes: multiply the decimal part by 60. 2.4 hours = 2 hours 24 minutes.
- On a calculator, the degrees-minutes-seconds key handles hours and minutes too.
Converting speeds
To go from m/s to km/h, multiply by 3600 (seconds in an hour) and divide by 1000 (metres in a kilometre), which is the same as multiplying by 3.6. To go back, divide by 3.6.
Average speed for a whole journey
Find the total distance and the total time, then divide. Do not average the two speeds, because the journey usually spends different amounts of time at each one.
How long does it take to travel 84 miles at 56 mph?
Show the answer
84 ÷ 56 = 1.5 hours, which is 1 hour 30 minutes.
Part 2 of 3: See it worked
Worked examples
Example 1
A car travels 135 km in 1 hour 30 minutes. Find its average speed in km/h.
- 1 hour 30 minutes = 1.5 hours
- speed = 135 ÷ 1.5
Answer: 90 km/h.
Example 2
Convert 20 m/s into km/h.
- In one hour: 20 × 3600 = 72 000 m
- 72 000 m = 72 km
Answer: 72 km/h.
Example 3
Leah cycles 60 km at 40 km/h, then 90 km at 60 km/h. Find her average speed for the whole journey.
- Time for part 1: 60 ÷ 40 = 1.5 h; part 2: 90 ÷ 60 = 1.5 h
- Total distance 150 km, total time 3 h
- 150 ÷ 3 = 50
Answer: 50 km/h.
Common mistakes
- Treating 1 hour 15 minutes as 1.15 hours. It is 1.25 hours.
- Averaging the two speeds instead of using total distance ÷ total time.
- Mixing units, such as a distance in metres with a time in hours.
- Dividing the wrong way round: speed is distance ÷ time, not time ÷ distance.
A force of 600 N acts on an area of 0.15 m². Find the pressure.
Show the answer
600 ÷ 0.15 = 4000 N/m² (4000 Pa).
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
How long does it take to travel 84 miles at 56 mph?
84 ÷ 56 = 1.5 hours, which is 1 hour 30 minutes.
A force of 600 N acts on an area of 0.15 m². Find the pressure.
600 ÷ 0.15 = 4000 N/m² (4000 Pa).
A block has mass 312 g and volume 40 cm³. Find its density.
312 ÷ 40 = 7.8 g/cm³.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
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