MathematicsExam code: 0580
Compound Measures
Number
Matching units before calculating
- Both quantities must be in units that match the answer required
- Convert first, then divide, since converting afterwards invites a second error
- A speed wanted in m/s needs the distance in metres and the time in seconds
- A rate given per hour becomes a rate per minute by dividing by 60, and the reverse by multiplying
Worked example
Changing km/h to m/s and back
A cyclist rides at 27 km/h. Write this speed in metres per second. A runner's speed is 4.5 m/s. Write this speed in km/h.
Solution:
- 27 km/h means 27 km travelled in 1 hour
- 27 km is 27 000 m, and 1 hour is 60 × 60 = 3600 seconds
- 27 000 ÷ 3600 = 7.5 m/s
- 4.5 m/s means 4.5 m travelled every second
- In 3600 seconds that is 4.5 × 3600 = 16 200 m
- 16 200 m is 16.2 km, so the speed is 16.2 km/h
- Check: 7.5 × 3.6 = 27 and 16.2 ÷ 3.6 = 4.5, and each m/s value is the smaller number