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Pumps A, B, and C

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by abhi332 » Wed Feb 24, 2010 11:57 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

[spoiler]OA: E[/spoiler]
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by firdaus117 » Wed Feb 24, 2010 12:05 pm
Assume total tank capacity be 60 units.
Rate of A+B=60/(6/5)=50 units/hr
Rate of B+C=60/(3/2)=40 units/hr
Rate of C+A= 60/2 = 30 units/hour
Add all,2(A+B+C)=120
Rate of A+B+C=60 units/hr
Hence,Time to fill tank by A,B,C=60/60=1 hr Option E
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by Pedros » Wed Feb 24, 2010 12:13 pm
A+B = 5/6 of the work / hour,
B+c = 1/2 of the work / hour-------------->1
A+C= 2/3 of the work / hour

a=2/3 -c , a = 5/6 - b

so 2/3-C = 5/6-B------------------->2

Since B = 1/2 -c , So sunbstitute in Eq. 2 : 2/3 -C = 5/6 - (1/2 - C)

2/3 - 5/6 + 1/2 = 2c

therefore the Rate of Pump C = 1/6
Substitute in ( 1) so B = 3/6

Finally A = 2/6

A+B+C = 1
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