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Pumps A, B and C operate at their respective constant rates.

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Pumps A, B and C operate at their respective constant rates. [#permalink] New post 16 Feb 2006, 10:59
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Pumps A, B and C operate at their respective constant rates. Pumps A and B operating simultaneously, can fill a certain tank in 6/5 hours; pumps A and C, operating simultaneously can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously can fill the tank in 2 hours. How many hours does it take pumps A, B, and C operating simultaneously to fill the tank.
A- 1/3
B- 1/2
C- 2/3
D- 5/6
E- 1
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 [#permalink] New post 16 Feb 2006, 12:57
1/a + 1/b = 5/6

1/b +1/c = 2/3

1/c + 1/a =1/2

add all of them together u get

1/a +1/b +1/c = 1

hence they can fill the tank in 1 hr
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 [#permalink] New post 16 Feb 2006, 17:58
1/A + 1/B = 5/6 -- (1)
1/A + 1/C = 2/3 -- (2)
1/B + 1/C = 1/2 -- (3)

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

(3) + (2)
2/B = 2/3
1/B = 1/3

1/3 + 1/C = 1/2
1/C = 1/6

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

1/A + 1/B + 1/C = 1
A + B + C = 1 hour

Ans E
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Re: Pumps A, B and C operate at their respective constant rates. [#permalink] New post 09 Dec 2011, 03:12
Rate of A + B = 5/6---------(i)
Rate of A + C = 2/3 --------(ii)
Rate of B + C = 1/2 --------(iii)
Adding (i), (ii) and (iii) Together
2(A + B +C) = 12/6 = 1

A, B and C took 1 hour.
Ans. E
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Re: Pumps A, B and C operate at their respective constant rates. [#permalink] New post 13 Mar 2012, 01:50
Could someone explain why we use the reciprocal here?

Thanks, alot!
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Re: Pumps A, B and C operate at their respective constant rates. [#permalink] New post 13 Mar 2012, 02:00
Expert's post
Re: Pumps A, B and C operate at their respective constant rates.   [#permalink] 13 Mar 2012, 02:00
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