Average speed of a 30/60 round trip

Question

You drive to a town at 30 km/h and return along the same road at 60 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. For two equal-distance legs, that is the harmonic mean of the speeds: \bar v = \frac{2 v1 v2}{v1 + v2} = \frac{2 	imes 30 	imes 60}{90} = \frac{3600}{90} = 40 	ext{ km/h}. Not 45. The slow leg takes twice as long as the fast leg, so it dominates the total time and pulls the average down toward 30. Sanity check with a concrete distance: 60 km each way is 2 h out (at 30) and 1 h back (at 60), so 120 km in 3 h = 40 km/h. Takeaway. Equal distances call for the harmonic mean, which sits below the arithmetic mean and closer to the slower rate. If …

Average speed of a 30/60 round trip

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