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

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MP
 Post subject: Pumps A, B and C operate at their respective constant rates
 Post Posted: Tue May 13, 2008 9:52 pm 
Pumps A, B and C operate at their respective constant rates. Pumps A and B, simultaneously, can fill a certain tank in 6/5 hours. Pump A and C, operating simultaneously, can fill the tank in 3/2 hours; abd 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

Correct answer: (E)

I am unable to deduce the correct solution.
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RonPurewal
 Post subject: Re: Some tough Math problems : problem 3
 Post Posted: Wed May 14, 2008 6:04 am 
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ManhattanGMAT Staff


Posts: 6765
MP wrote:
Pumps A, B and C operate at their respective constant rates. Pumps A and B, simultaneously, can fill a certain tank in 6/5 hours. Pump A and C, operating simultaneously, can fill the tank in 3/2 hours; abd 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

Correct answer: (E)

I am unable to deduce the correct solution.


remember that rate = reciprocal of time taken to complete one job.
also, remember that rates are additive, so rate(pumps a AND b) = rate(pump a) + rate(pump b).
so:
rate(pumps a AND b) = 5/6
rate(pumps a AND c) = 2/3
rate(pumps b AND c) = 1/2

using the above fact about additive rates,
rate(pump a) + rate(pump b) = 5/6
rate(pump a) + rate(pump c) = 2/3
rate(pump b) + rate(pump c) = 1/2

you know you want the rate for all three pumps. from the symmetry of the above equations, it becomes apparent that we can find this by adding together all 3 equations:
2rate(pump a) + 2rate(pump b) + 2rate(pump c) = 5/6 + 2/3 + 1/2 = 2
rate(pump a) + rate(pump b) + rate(pump c) = 1
rate(pumps a AND b AND c) = 1 (because rates are additive)
time = reciprocal of 1 = 1
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MP
 Post subject: Thanks!
 Post Posted: Wed May 14, 2008 6:25 am 
Thanks a lot! I kept doing a lot of calculations and got things wrong.

I assumed that let A, B, C complete the job (indivisually) in a, b, c hours.

Hence their respective rates would be: 1/a, 1/b, 1/c

Then,
1/a + 1/b = 5/6
1/a + 1/c = 2/3
1/b + 1/c = 1/2

Then I was solving the 3 equations to get values of a, b, c. That consumed a lot of time and I had to guess the answer.
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rfernandez
 Post subject:
 Post Posted: Thu May 15, 2008 6:50 pm 
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Course Students


Posts: 386
We're glad it makes sense now.
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gordon.thomas
 Post subject: Re: Pumps A, B and C operate at their respective constant rates
 Post Posted: Mon Oct 05, 2009 3:11 pm 
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Course Students


Posts: 1
Answer should be (E) = 2 hours

In 1 hour, Pump A can empty 1/2 of the tank (it is already 1/2 full)
In 1 hour, Pump B can empty 1/3 of the tank

Since, pump A and B empty the tank together, and assume A alone empties all the water that is present (since it's half full), the problem reduces to how long can Pump C take to fill that much of the tank which B can empty. In 1 hour B can empty 1/3 of the tank.

In 1 hour, Pump C can fill 1/6 of the tank. Thus in 2 hours, C can fill 1/3 of the tank.

Hence in 2 hours, B removes everything that C fills and A removes whatever is present in the tank
[editor: this is apparently an answer to a completely different problem.]
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RonPurewal
 Post subject: Re: Pumps A, B and C operate at their respective constant rates
 Post Posted: Sat Oct 24, 2009 7:15 am 
Offline
ManhattanGMAT Staff


Posts: 6765
gordon.thomas wrote:
Answer should be (E) = 2 hours

In 1 hour, Pump A can empty 1/2 of the tank (it is already 1/2 full)
In 1 hour, Pump B can empty 1/3 of the tank

Since, pump A and B empty the tank together, and assume A alone empties all the water that is present (since it's half full), the problem reduces to how long can Pump C take to fill that much of the tank which B can empty. In 1 hour B can empty 1/3 of the tank.

In 1 hour, Pump C can fill 1/6 of the tank. Thus in 2 hours, C can fill 1/3 of the tank.

Hence in 2 hours, B removes everything that C fills and A removes whatever is present in the tank


what question are you answering?
certainly not the one in this thread.
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