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GMAT PREP PS question

by alex.gellatly » Tue Apr 17, 2012 6:55 pm
A boat traveled upstream a distance of 90 miles at an average speed of (v - 3) miles per hour and then traveled the same distance downstream at an average speed of (v + 3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

(A) 2.5
(B) 2.4
(C) 2.3
(D) 2.2
(E) 2.1

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by GMATGuruNY » Tue Apr 17, 2012 7:21 pm
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by Anurag@Gurome » Tue Apr 17, 2012 7:54 pm
alex.gellatly wrote:A boat traveled upstream a distance of 90 miles at an average speed of (v - 3) miles per hour and then traveled the same distance downstream at an average speed of (v + 3) miles per hour. If the trip upstream took half an hour longer than the trip downstream, how many hours did it take the boat to travel downstream?

(A) 2.5
(B) 2.4
(C) 2.3
(D) 2.2
(E) 2.1

Thanks
Time taken to travel upstream = 90/(v - 3) hr
Time taken to travel downstream = 90/(v + 3) hr

Traveling upstream took 1/2hr more than downstream.
So, 90/(v - 3) = 90/(v + 3) + 1/2
180(v + 3) = 180(v - 3) + (v² - 9)
1080 = v² - 9 or v = √1089 = 33

Speed for downstream = 33 + 3 = 36 mph
Therefore, time taken to travel downstream = 90/36 = 2.5 hrs

The correct answer is A.
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