Maya drives from New York City to Boston at a rate of 40 MPH and drives at a rate of 60 MPH on the return trip. What was his average speed for the entire trip? Use the Harmonic mean to compute? Construct the HM geometrically?
The Average Speed is
Suppose that the distance between New York City and Boston is
Time reqd. for this trip, at the rate of
The return journey is at the rate of
Thus, total distance of
Hence, the Average Speed for the complete journey is given by,
Those who are familiar with Harmonic Mean will, at a glance, say
that the Average Speed for the trip is not the Arithmetic Mean
but the Harmonic Mean of the speeds.
Numerically, the Average Speed is