MathematicsExam code: 0580
Compound Measures
Number
The relationship
- Speed is distance divided by time, and in this context "speed" always means average speed
- The three arrangements follow from one another
| To find | Calculate |
|---|---|
| Speed | distance ÷ time |
| Distance | speed × time |
| Time | distance ÷ speed |
- Common units are metres per second (m/s) and kilometres per hour (km/h)
- A journey made in stages needs total distance divided by total time, not an average of the separate speeds
Time in hours
- Time must be expressed in the unit the answer requires, and part-hours are decimals of an hour rather than minutes written after a point
- 1 hour 48 minutes is 1.8 hours, because 48 minutes is 48/60 of an hour
- Writing 1.48 instead is a common error in these questions
Worked example
Average speed with a part-hour
A car travels 153 km in 1 hour 48 minutes. Find its average speed in km/h.
Solution:
- Convert the time to hours: 48 ÷ 60 = 0.8, so the time is 1.8 hours
- Speed is distance divided by time: 153 ÷ 1.8
- The average speed is 85 km/h
- Check by reversing: 85 × 1.8 = 153
Exam tip
Check the time unit in speed and rate answers
In speed and rate questions, a correct value with the time in the wrong unit kept two of the three marks: a distance from a km/h graph with the time still in minutes, a time left in seconds or decimal minutes for an answer in minutes and seconds, and decimal hours for hours and minutes. Check the answer line's units before you finish, and turn a decimal part back with × 60: 3.35 hours is 3 hours 21 minutes.