Stage 10 · Percentages & speed
Average speed
Total distance ÷ total time.
How to do it
Method
Total distance ÷ total time
(120 + 90) ÷ (2 + 3) = 210 ÷ 5 = 42
One more example
120 km each way: 120 ÷ 60 = 2, 120 ÷ 40 = 3, 240 ÷ 5 = 48
In full
Average speed = total distance ÷ total time. 120 km in 2 hours, then 90 km in 3 hours: total distance 120 + 90 = 210 km, total time 2 + 3 = 5 hours, average speed = 210 ÷ 5 = 42 km/h. Where a leg gives only its speed and time, find its distance first with speed × time: 60 km/h for 2 hours is 60 × 2 = 120 km. Careful: the average speed is usually not the mean of the two speeds. A and B are 120 km apart; there at 60 km/h, back at 40 km/h: there takes 120 ÷ 60 = 2 hours, back 120 ÷ 40 = 3 hours, there and back is 120 × 2 = 240 km, total time 2 + 3 = 5 hours, average speed = 240 ÷ 5 = 48 km/h, not (60 + 40) ÷ 2 = 50 km/h. The slower way back takes longer, so the average sits nearer the slower speed; only when the two legs take the same time is the average speed the mean of the two.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Average speed = ? km/h
Show the answer and working
Answer: Average speed = 39 km/h
Average speed = total distance ÷ total time: there takes 78 ÷ 26 = 3 h, there and back is 78 × 2 = 156 km, total time 3 + 1 = 4 h, 156 ÷ 4 = 39 km/h
Example 2
Average speed = ? km/h
Show the answer and working
Answer: Average speed = 70 km/h
Average speed = total distance ÷ total time: leg 2 is 100 × 5 = 500 km, total distance 60 + 500 = 560 km, total time 3 + 5 = 8 h, 560 ÷ 8 = 70 km/h
Example 3
Average speed = ? km/h
Show the answer and working
Answer: Average speed = 55 km/h
Average speed = total distance ÷ total time: leg 1 is 45 × 3 = 135 km, total distance 135 + 140 = 275 km, total time 3 + 2 = 5 h, 275 ÷ 5 = 55 km/h
Example 4
Average speed = ? m/min
Show the answer and working
Answer: Average speed = 60 m/min
Average speed = total distance ÷ total time: there takes 660 ÷ 55 = 12 min, back takes 660 ÷ 66 = 10 min, there and back is 660 × 2 = 1320 m, total time 12 + 10 = 22 min, 1320 ÷ 22 = 60 m/min (not the mean of the two speeds: the slower way takes longer)
Practise average speed in the game →Stage 10 · Percentages & speed · Free to start, unlimited questions, no download