megafan wrote:
A car travels from Town A to Town B at an average speed of 40 miles per hour, and returns immediately along the same route at an average speed of 50 miles per hour. What is the average speed in miles per hour for the round-trip?
(A) \(45\frac{4}{9}\) mph
(B) 44 mph
(C) 45 mph
(D) \(44\frac{4}{9}\) mph
(E) \(44\frac{1}{9}\) mph
Hi,
This is a classic question on Speed, time, & distance.
1. When time traveled in each segment is constant, then average speed is simple mean of speeds.
2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.
So this question falls in the category of 2.
=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.
=> Average speed = Reciprocal of mean of 1/40 & 1/50.
=> Average speed = Reciprocal of (1/40 + 1/50)/2 = Reciprocal of (5+4)/400 = 44 4/9 .
-Shalabh
When distance traveled in each segment is constant, then average speed simply be \(\frac{2xy}{x+y}\), where x and y are speeds.\(\frac{2*40*50}{40+50}\) = \(44\frac{4}{9}\)