Speed · Usually met around P6
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. If part of the journey 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. You go there at 60 km/h and come back at 40 km/h. Going takes 120 ÷ 60 = 2 hours, and coming back takes 120 ÷ 40 = 3 hours. There and back is 120 × 2 = 240 km, and the total time is 2 + 3 = 5 hours. So the average speed = 240 ÷ 5 = 48 km/h, not (60 + 40) ÷ 2 = 50 km/h. The slower trip back takes longer, so the average is closer to the slower speed. The average speed is the mean of the two speeds only when both parts take the same time.
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 = 40 km/h
Average speed = total distance ÷ total time: there takes 100 ÷ 100 = 1 h, there and back is 100 × 2 = 200 km, total time 1 + 4 = 5 h, 200 ÷ 5 = 40 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 1 is 100 × 4 = 400 km, total distance 400 + 160 = 560 km, total time 4 + 4 = 8 h, 560 ÷ 8 = 70 km/h
Example 3
Average speed = ? m/min
Show the answer and working
Answer: Average speed = 80 m/min
Average speed = total distance ÷ total time: leg 2 is 50 × 8 = 400 m, total distance 720 + 400 = 1120 m, total time 6 + 8 = 14 min, 1120 ÷ 14 = 80 m/min
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