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 findCalculate
Speeddistance ÷ time
Distancespeed × time
Timedistance ÷ speed
A triangle divided into three cells with distance across the top and speed and time side by side underneath, so covering the quantity being found leaves the calculation for it: distance over time, distance over speed, or speed multiplied by time
Source: Compound measures by Save My Exams
  • 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 the single most common error in these questions
Exam tip

The speed, distance and time relationship is not in the List of formulas, so it has to be known — the syllabus says so directly, and these quantities appear in 17 of the 43 papers. Check the units match before substituting: a speed in km/h with a time in minutes needs one of them converted first.

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