GMAT Upstream Downstream

Hello I am preparing for GMAT so can anybody explain me the GMAT Upstream Downstream give me the feedback please ??

As you want to understand the GMAT Upstream Downstream

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 half an hour longer than downstream, how many hours did it take the boat to travel downstream?

(*) 2.5
(*) 2.4
(*) 2.3
(*) 2.2
(*) 2.1


Upstream: V-3 miles per hour
Downstream : V+3 miles per hour
Distance: 90 miles
Hence,
Time_Upstream = 90/(V-3)
Time_Downstream = 90/(V+3)
Now, it says that

Time_Upstream = 1/2 + Time_Downstream

i.e
90/(V-3) = 1/2 + 90/(V+3)

You can do the following way also :-

Upstream R=v-3 T=t+.5 D = 90
Downstream R=v+3 T=t D = 90

1.) (v-3)(t+.5)= 90
2.) (v+3)(t) = 90

Set both equations equal
(v-3)(t+.5) = (v+3)(t)
multiplying through and solving for v in terms of t will get you:
v-3 = 12t

plug this into the first equation and you will get:
12t(t+.5) = 90
12t^2 + 6t = 90 you can take out 6 to make everything come out in whole numbers:
2t^2 + t - 15 = 0
(2t -5)(t+3) = 0
t = 5/2 or -3

5/2 = 2.5

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Answered By StudyChaCha Member