Using the speed-distance-time relationship to find any one quantity, average speed, and converting between mph and km/h and between hours and minutes.

What this dot point is asking

CCEA wants you to use the speed-distance-time relationship to find any one of the three quantities, to calculate an average speed, and to convert between units (minutes to hours, and mph to km/h). Motoring mathematics is a whole content area of Unit 1, and speed-distance-time is the most common calculation.

The answer

The speed-distance-time relationship

A useful memory aid is the D-S-T triangle: with D on top and S and T below. Cover the quantity you want: cover D to get $S \times T$; cover S to get $D \div T$; cover T to get $D \div S$.

Average speed

Getting the units right

The single biggest source of errors is time:

• 40 minutes is not 0.40 hours. Convert minutes to hours by dividing by 60: $40 \div 60 = \tfrac{2}{3}\ \text{h} \approx 0.667\ \text{h}$.
• 2 h 30 min $= 2.5\ \text{h}$; 2 h 15 min $= 2.25\ \text{h}$.

To convert speeds, use the approximate rule 5 miles ≈ 8 kilometres, so to change mph to km/h multiply by $\tfrac{8}{5} = 1.6$, and to change km/h to mph divide by 1.6. For distances the same rule applies: 10 miles is about 16 km.

Reading a time as hours and minutes

Calculations often give a decimal time that you must turn back into hours and minutes. The decimal part is a fraction of an hour, so multiply it by 60 to get the minutes. For example, $2.25\ \text{h}$ is 2 hours and $0.25 \times 60 = 15$ minutes, and $1.5\ \text{h}$ is 1 hour 30 minutes. A time of $0.75\ \text{h}$ is $0.75 \times 60 = 45$ minutes.

Worked example: a journey in two parts

Worked example: finding the time for a journey

Examples in context

Example 1. Planning arrival time. Travelling 120 miles at an average of 48 mph takes $120 \div 48 = 2.5$ hours, so a driver leaving at 09:00 arrives about 11:30.

Example 2. Reading a speed in km/h. A 50 km/h limit is about $50 \div 1.6 \approx 31$ mph, close to the 30 mph urban limit.

Try this

Q1. A car travels 80 miles in 2 hours. What is its average speed? [1 mark]

• Cue. $80 \div 2 = 40$ mph.

Q2. Convert 1 hour 15 minutes into hours. [1 mark]

• Cue. 1.25 hours.

Q3. A car travels at 60 km/h for 30 minutes. How far does it go? [2 marks]

• Cue. $60 \times 0.5 = 30$ km.