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Distance/Time

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by hypik21 » Wed Dec 17, 2008 4:36 pm
A boat traveled upstream at a distance of 90 miles at v-3 mph and downstream, the same distance at v+3 mph. If the trip upstream took 30 mins more than the trip downstream, how many hours did it take the boat to travel downstream?

OA : 2.5
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by cramya » Wed Dec 17, 2008 4:59 pm
Up stream

Distance - > 90
speed-> v-3
time-> t+1/2 = 2t+1/2

90 = 2t+1/2 (v-3)

180/(2t+1) - 3 = v (1)

Downstream
Distance - > 90
speed-> v+3
time-> t

90 = t(v+3)

90/t-3 = v (2)


Equate both v's from 1) and 2)


180/(2t+1) - 3 = 90/t-3

4t^2+2t-30 = 0

t=2.5
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Re: Distance/Time

by logitech » Wed Dec 17, 2008 6:10 pm
[90/(v-3)-90/(v+3)] = 1/2 hr

V=33

tdown = 90/36 = 2.5 hrs
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by vittalgmat » Wed Dec 17, 2008 7:49 pm
Here is a link in GMAT Resources page which explains how to handle
such kind of problems.

https://www.beatthegmat.com/two-methods- ... t6749.html

HT Helps
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by Abdulla » Wed Dec 17, 2008 8:34 pm
cramya wrote:Up stream

Distance - > 90
speed-> v-3
time-> t+1/2 = 2t+1/2

90 = 2t+1/2 (v-3)

180/(2t+1) - 3 = v (1)

Downstream
Distance - > 90
speed-> v+3
time-> t

90 = t(v+3)

90/t-3 = v (2)


Equate both v's from 1) and 2)


180/(2t+1) - 3 = 90/t-3

4t^2+2t-30 = 0

t=2.5
cramya, something wrong with your calculation, I'm confused ..

let me do it step by step..

up : v-3= 90/(t+1/2)
v = 90/(t+1/2) +3 (not -3)
v = 180/(t+1) +3 ------(1)

down: v+3= 90/t
v= 90/t -3 ----------(2)

180/(t+1)+3 = 90/t-3
180/(t+1)+9 = 90/t
180t/(t+1)+ 9t = 90
180t + 18t^2+9t =180t+90
18t^2+9t-90 = 0
2t^2+t-10=0 until here and I stopped.. could you tell me what is wrong??
Abdulla
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