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?

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Answer 1 · 2016-08-26T17:11:35

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

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.!