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megafan
Joined: 28 May 2009
Last visit: 15 Oct 2017
Posts: 137
Given Kudos: 91
Location: United States
Concentration: Strategy, General Management
Schools: Stern PT Fall'18 Booth PT '18
GMAT Date: 03-22-2013
GPA: 3.57
WE:Information Technology (Consulting)
05 Jan 2013, 18:08
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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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
(A) \(45\frac{4}{9}\) mph
(B) 44 mph
(C) 45 mph
(D) \(44\frac{4}{9}\) mph
(E) \(44\frac{1}{9}\) mph
PrashantPonde
Joined: 27 Jun 2012
Last visit: 29 Jan 2025
Posts: 311
Given Kudos: 185
Concentration: Strategy, Finance
Schools: Haas EWMBA '17
05 Jan 2013, 18:47
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Using "Pick numbers" strategy, assume total distance as 200 miles. (LCM of 40 & 50)
Time taken to travel from A to B = 200/40 = 5 hours
Time taken to travel from B to A = 200/50 = 4 hours
\(Average(speed) = \frac{{Total (Distance) }}{{ Total (Time) }}= \frac{(200+200)}{(5+4)} = \frac{400}{9} = 44 \frac{4}{9}\)
Hence Choice(D).
Time taken to travel from A to B = 200/40 = 5 hours
Time taken to travel from B to A = 200/50 = 4 hours
\(Average(speed) = \frac{{Total (Distance) }}{{ Total (Time) }}= \frac{(200+200)}{(5+4)} = \frac{400}{9} = 44 \frac{4}{9}\)
Hence Choice(D).
08 Jan 2013, 02:07
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megafan
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
