Question

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?

Answer 1

The Average Speed is `48 "mph"`.

Explanation:

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

trip.

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.!