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

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Manager
Joined: 02 Oct 2006
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Pumps A,B, and C operate at constant rates. Pumps A & B, [#permalink]  12 Nov 2006, 07:28
4. Pumps A,B, and C operate at constant rates. Pumps A & 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 full the tanks in 2 hours. How many hours dies it take pumps A,B, and C operating simultaneously to fill the tank?

a) 1/3
b) Â½
c) 2/3
d) 5/6
e) 1
Manager
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Would be great if anyone could explain how to get to the answer

My gmat is tomorrow!!!!!!!
GMAT Instructor
Joined: 04 Jul 2006
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Clue: How long would it take for LOTS 1,2, And 3 to do the job?

LOT 1= 1 A AND 1 B
VP
Joined: 28 Mar 2006
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In 1hr

2[A+B+C] = 5/6+2/3+1/2

A+B+C = 1

So they do it in 1 hr
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Pump A - 1 tank in A hours --> 1/A tank in 1 hour
Pump B - 1 tank in B hours --> 1/B tank in 1 hour
Pump C - 1 tank in C hours --> 1/C tank in 1 hour

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

Then (1) - (2)
1/B - 1/C = 1/6 --- (3)
1/B + 1/C = 1/2 --- (4)

Then (3) + (4)
2/B = 2/3
B = 3

Substitute B = 3 to (4), we get C = 6

Substitute C = 6 to (2), we get A = 2

So together, they will take ABC/(AB + AC + BC) hours = 36/36 = 1 hour
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