← LabsMath 6 · rate-speed

Average-speed trap

Why you cannot average speeds.

60 km/h
1 h
40 km/h
2 h
time (h)km140 km in 3 h

Black: the trip, leg by leg. Red dashed: one straight line from start to finish — its slope is the average speed.

Average of the speeds
50
(60 + 40) ÷ 2
Average speed
46.7
140 km ÷ 3 h

They differ by 3.3 km/h. The slower leg (40 km/h) takes 2 of the 3 hours, so the true average sits below the mean of the speeds. Average speed is total distance over total time — always.

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