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Pumps A, B, and C

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by gmatblood » Wed Nov 02, 2011 3:38 am
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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by user123321 » Wed Nov 02, 2011 4:03 am
gmatblood wrote: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
A+B does 5/6th in 1 hr
B+C does 2/3rd in 1 hr
C+A does 1/2th in 1 hr

so In one hour the above fractions when added
2A + 2B + 2C does 5/6+2/3+1/2 = 2 times work in 1hr

so 2A + 2B + 2C takes 1/2 hr for doing 1 work
=> A+B+C takes 1/2*2 = 1 hr for doing 1 work.

is it E?

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by GMATGuruNY » Wed Nov 02, 2011 4:26 am
I posted a solution here:

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