Average speed of a 60/40 round trip

Question

You drive to a destination at 60 km/h and return along the same route at 40 km/h. Solve in your head. What is your average speed for the round trip? Aim: under 10 seconds.

Accepted Answer

Average speed is total distance over total time, which for equal distances is the harmonic mean: \bar v = \frac{2 v1 v2}{v1 + v2} = \frac{2 	imes 60 	imes 40}{100} = \frac{4800}{100} = 48 	ext{ km/h}. Not 50. The slower leg takes longer, so it drags the average below the midpoint. Sanity check with a concrete distance: 120 km each way takes 2 h out, 3 h back, 240 km in 5 h = 48 km/h. Takeaway. Equal distances 	o harmonic mean; equal times 	o arithmetic mean. The harmonic mean is always below the arithmetic mean, so if your answer to a round-trip question is the simple midpoint, it's wron…

Average speed of a 60/40 round trip

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