GMAT PREP PS question

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

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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Source: Beat The GMAT — Problem Solving | Tue Apr 17, 2012 6:55 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 17, 2012 7:21 pm

I posted a solution here:

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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) + (vÂ² - 9)
1080 = vÂ² - 9 or v = âˆš1089 = 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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