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?

1 Answer
Aug 26, 2016

The Average Speed is #48 "mph"#.


Suppose that the distance between New York City and Boston is

#x# miles.

Time reqd. for this trip, at the rate of #40 "mph, is," x/40# hours.

The return journey is at the rate of #60 "mph, so," x/60# hours for this


Thus, total distance of #2x# miles was covered in

#x/40+x/60# hours.

Hence, the Average Speed for the complete journey is given by,

Distance/Time, i.e.,

#(2x)/(x/40+x/60)=2/(1/40+1/60)# mph.

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 #(2*60*40)/(60+40)=48"mph."#

Enjoy Maths.!