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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
Posts: 49
A boat traveled upstream a distance of 90 miles at an  [#permalink]

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Updated on: 10 Feb 2014, 12:34
7
41
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Difficulty:

55% (hard)

Question Stats:

75% (01:55) correct 25% (02:02) wrong based on 514 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

Originally posted by CfaMiami on 23 Jul 2006, 08:02.
Last edited by Bunuel on 10 Feb 2014, 12:34, edited 1 time in total.
Edited the question and added the OA.
Manager
Joined: 02 Apr 2006
Posts: 152

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23 Jul 2006, 08:41
2
3
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
Director
Joined: 28 Dec 2005
Posts: 702

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23 Jul 2006, 13:11
90/(v-3)=0.5+90/(v+3)

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

A
SVP
Joined: 30 Mar 2006
Posts: 1661

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26 Jul 2006, 01:39
3
2
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
Intern
Joined: 17 Jan 2010
Posts: 24
Re: GMAT PREP PS Boat (Upstream vs Downstream)  [#permalink]

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24 Jan 2010, 02:51
it took me a while, but i finally got it
Manager
Joined: 22 Jan 2010
Posts: 108
Schools: UCLA, INSEAD
Re: GMAT PREP PS Boat (Upstream vs Downstream)  [#permalink]

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24 Jan 2010, 08:50
I forgot to take account for both directions. I add the current on one but forgot to subtract it from the other.
Math Expert
Joined: 02 Sep 2009
Posts: 52284
Re: A boat traveled upstream a distance of 90 miles at an  [#permalink]

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10 Feb 2014, 12:34
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15
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.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-boat-traveled-upstream-90-miles-at-an-average-speed-of-100767.html
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Joined: 16 Oct 2010
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Re: A boat traveled upstream a distance of 90 miles at an  [#permalink]

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10 Feb 2014, 21:12
3
1
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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Posts: 9427
Re: A boat traveled upstream a distance of 90 miles at an  [#permalink]

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26 Jul 2018, 11:17
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Re: A boat traveled upstream a distance of 90 miles at an &nbs [#permalink] 26 Jul 2018, 11:17
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