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# GMAT PREP WORD PROBLEM!!!

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Intern
Joined: 04 May 2006
Posts: 15

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14 Jun 2006, 20:17
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Any takers on this problem. Seems simple but i got it wrong. Please explain. Thanks

Pumps A,B and C operate simultaneously at their respective constant rates, A&B simultaneously can fill a tank in 6/5hrs, A&C in 3/2 hrs and B&C 2hrs. How many hrs simultaneously? together... answer =1hr explain please...
Intern
Joined: 14 Jun 2006
Posts: 4
Re: GMAT PREP WORD PROBLEM!!! [#permalink]

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14 Jun 2006, 20:34
salama wrote:
Any takers on this problem. Seems simple but i got it wrong. Please explain. Thanks

Pumps A,B and C operate simultaneously at their respective constant rates, A&B simultaneously can fill a tank in 6/5hrs, A&C in 3/2 hrs and B&C 2hrs. How many hrs simultaneously? together... answer =1hr explain please...

given the equations:

(1/A+1/B)=5/6 --> 1/B=5/6-1/A (1)
(1/A+1/C)=2/3 --> 1/C=2/3-1/A (2)
(1/B+1/C)=1/2 (3)

solve them to find 1/A+1/B+1/C:

use (1) and (2) in (3):

5/6-1/A+2/3-1/A=1/2
1/A=1/2

thus 1/B=5/6-1/2=1/3
1/C=2/3-1/2=1/6

finally (1/A+1/B+1/C)t =1
(1/2+1/3+1/6)t = 1

so t=1 hour
VP
Joined: 02 Jun 2006
Posts: 1260

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14 Jun 2006, 20:57
Let
Ra = rate of filling for A per hr.
Rb = rate of filling for B per hr
Rc = rate of filling for C per hr

Given
1/(Ra+Rb) = 6/5 => (Ra+Rb) = 5/6
1/(Ra+Rc) = 3/2 => (Ra+Rc) = 2/3
1/(Rb+Rc) = 2 => (Rb+Rc) = 1/2

2(Ra+Rb+Rc) = 5/6+2/3+1/2
= 5/6+4/6+3/6
= 12/6 = 2

=> (Ra+Rb+Rc) = 1 tank/hr

Time to fill = 1/(Ra+Rb+Rc) = 1hr.
SVP
Joined: 30 Mar 2006
Posts: 1728

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14 Jun 2006, 23:41
1/A + 1/B = 5/6
1/A + 1/C = 2/3

hence 1/B - 1/C = 1/6
also 1/B + 1/C = 1/2

Hence 1/B = 1/3 or B takes 3 hrs
1/A = 1/2 and 1/C = 1/6

Together = 1/A + 1/B +1/C
= 1/2 + 1/3 + 1/6

= 1 hr
Director
Joined: 06 May 2006
Posts: 791

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14 Jun 2006, 23:57
1 hr. Used haas_mba07's method.

Rgds,
14 Jun 2006, 23:57
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