A Simple Math Bar Bet (Harmonic Mean)

What is the average of 20 miles per hour and 60 miles per hour? Well, it’s (20 + 60) / 2 = 40 miles-per-hour, right? Wrong.

This is one of my favorite little math problems. The average of 20 mph and 60 mph is 30m mph, not 40 mph. Suppose the distance between points A and B is 120 miles. You drive from A to B at 20 mph. It will take you 6 hours. Now you turn around and drive from B to A at 60 mph. It will take you 2 hours. So your total distance traveled is 240 miles and your time was 8 hours. Your average speed was 240 / 8 = 30 mph.

To calculate the average of two rates, it’s better to use the harmonic mean. The harmonic mean of x and y = 2 / (1/x + 1/y).

A neat little problem that many people don’t know about. Very useful as a bar bet!


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