Gotta be a simpler way...Work problem

[LPP]

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

Official Answer:

SPOILER: a

This one seemed simple at first but gave me a pretty hard time. Finally got it by plugging numbers from the answer choices...Does anybody know of a simpler method to go about solving this one??

[bm_gmat]

My answer is A.

90/(V-3) - 90/(V+3) = 1/2
=> 90{6/(V^2 - 9)} = 1/2
=> V^2 - 9 = 90*6*2
=> V^2 = 90*6*2 + 9
=> V^2 = 9(120 + 1) = 9*121

therefore, V = 3*11 = 33

So, the time taken = 90/(33+3) = 90/36 = 2.5

[LPP]

Thanks bm.