Where is the Harmonic mean used?

Question

There is a mean called Harmonic mean. http://dlmf.nist.gov/1.2#E19

I mostly see usage of arithematic mean and geometric mean. On the other hand, I have never seen the usage of Harmonic mean yet.

In what kind of case, is the Harmonic mean used?

Answer 1

You go on a round trip. You go out at $50$ miles per hour and come back at $60$ miles per hour. The average speed of your whole trip will be the harmonic mean of $50$ and $60$ (mph). You can extend this to several legs of a trip all the same length. Your overall average speed will be the harmonic mean of the speeds on the various legs of the trip.