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

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Manager
Joined: 13 Dec 2005
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Pumps A, B and C operate at their respective rates. Pumps A [#permalink]  18 Dec 2005, 20:46
Pumps A, B and C operate at their respective 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 same tank in 3/2 hours. Pumps B and C can fill the tank in 2 hours. How many hours will it take to fill the tank if all three are operating simultaneously?

I know the equation for this is usually 1/A alone + 1/B alone + 1/C alone =1/hours...but how do you find A or B or C by themselves? I can't make the math work.

PS - The book answer is 1 hour.
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Joined: 14 Sep 2005
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Location: South Korea
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From the stem, we get the below three equtations;

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

Question) 1/A + 1/B + 1/C = 1/X. What is X?

We combine the three equtations and we get the following equtation;
2 * (1/A + 1/B + 1/C) = 5/6 + 4/6 + 3/6 = 12/6 = 2/1
1/A + 1/B + 1/C = 1/1

Therefore, the number of hours taken for all three pumps is ONE.
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