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

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Intern
Joined: 06 Jan 2006
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Pumps A, B and C operate at their respective constant rates. [#permalink]

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16 Feb 2006, 11:59
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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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Manager
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16 Feb 2006, 13:57
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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16 Feb 2006, 18:58
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]

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09 Dec 2011, 04:12
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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Manager
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Re: Pumps A, B and C operate at their respective constant rates. [#permalink]

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13 Mar 2012, 02:50
Could someone explain why we use the reciprocal here?

Thanks, alot!

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Math Expert
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Re: Pumps A, B and C operate at their respective constant rates. [#permalink]

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13 Mar 2012, 03:00
Impenetrable wrote:
Could someone explain why we use the reciprocal here?

Thanks, alot!

Check this: pumps-a-b-and-c-operate-at-their-respective-constant-rates-91124.html (Solution and general concept)
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Kudos [?]: 124217 [0], given: 12076

Re: Pumps A, B and C operate at their respective constant rates.   [#permalink] 13 Mar 2012, 03:00
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