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# A boat traveled upstream a distance of 90 miles at an

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Current Student
Joined: 06 Sep 2005
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A boat traveled upstream a distance of 90 miles at an [#permalink]

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23 Jul 2006, 09:02
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Difficulty:

55% (hard)

Question Stats:

74% (02:07) correct 26% (02:18) wrong based on 480 sessions

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A boat traveled upstream 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 a half hour longer than the trip downstream, then 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-boat-traveled-upstream-90-miles-at-an-average-speed-of-100767.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Feb 2014, 13:34, edited 1 time in total.
Edited the question and added the OA.

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Manager
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23 Jul 2006, 09:41
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90/(V-3) = 90/(V+3) + 0.5 hours
=> 90(V+3) = (V-3) [90 + 0.5 V + 1.5]

90V + 270 = (V-3)(183/2 + V/2)
180V + 540 = (V-3)(183+V)= 183V- 549+ V^2 -3V

V^2 - 1089= 0 => V= 33 miles/hr

=> Time downstream = 90/36 = 30/12= 5/2= 2.5 hrs

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Director
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23 Jul 2006, 14:11
90/(v-3)=0.5+90/(v+3)

solve for v=33
Then, Td=90/36=2.5

A

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SVP
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26 Jul 2006, 02:39
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A

Time taken upstream = 90/v-3
Time taken downstream = 90/v+3

Hence

90/v-3 + 90/v+3 = 1/2

v = 33

Time taken downstream = 90/36 = 5/2 = 2.5 hrs

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Intern
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Re: GMAT PREP PS Boat (Upstream vs Downstream) [#permalink]

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24 Jan 2010, 03:51
it took me a while, but i finally got it

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Manager
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Re: GMAT PREP PS Boat (Upstream vs Downstream) [#permalink]

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24 Jan 2010, 09:50
I forgot to take account for both directions. I add the current on one but forgot to subtract it from the other.

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Manager
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Re: GMAT PREP PS Boat (Upstream vs Downstream) [#permalink]

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21 Oct 2011, 11:00
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http://www.beatthegmat.com/boat-traveled-t18353.html
Beautiful solution
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Re: A boat traveled upstream a distance of 90 miles at an [#permalink]

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10 Feb 2014, 10:07
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Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A boat traveled upstream a distance of 90 miles at an [#permalink]

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10 Feb 2014, 13:34
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A boat traveled upstream 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 a half hour longer than the trip downstream, then 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

Trip upstream took $$\frac{90}{v-3}$$ hours and trip downstream took $$\frac{90}{v+3}$$ hours. Also given that the difference in times was $$\frac{1}{2}$$ hours --> $$\frac{90}{v-3}-\frac{90}{v+3}=\frac{1}{2}$$;

$$\frac{90}{v-3}-\frac{90}{v+3}=\frac{1}{2}$$ --> $$\frac{90(v+3)-90(v-3)}{v^2-9}=\frac{1}{2}$$ --> $$\frac{90*6}{v^2-9}=\frac{1}{2}$$ --> $$v^2=90*6*2+9$$ --> $$v^2=9*(10*6*2+1)$$ --> $$v^2=9*121$$ --> $$v=3*11=33$$;

Trip downstream took $$\frac{90}{v+3}=\frac{90}{33+3}=2.5$$ hours.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-boat-traveled-upstream-90-miles-at-an-average-speed-of-100767.html
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Re: A boat traveled upstream a distance of 90 miles at an [#permalink]

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10 Feb 2014, 22:12
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CfaMiami wrote:
A boat traveled upstream 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 a half hour longer than the trip downstream, then 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-boat-traveled-upstream-90-miles-at-an-average-speed-of-100767.html

Here is a post discussing how to solve such equations easily: http://www.veritasprep.com/blog/2013/03 ... culations/
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Kudos [?]: 17408 [3], given: 232

Re: A boat traveled upstream a distance of 90 miles at an   [#permalink] 10 Feb 2014, 22:12
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