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# Someone please solve the PS problem in a quick way possible!

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Intern
Joined: 23 Jun 2009
Posts: 47

Kudos [?]: 28 [0], given: 6

Someone please solve the PS problem in a quick way possible! [#permalink]

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22 Jul 2009, 00:28
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I have solved it, but it took me close to 3 minutes due to long algebra. I wonder whether there is someone who could please try solving it, taking about 2 minutes, and just walk me through his/her efficient steps. Thanks.

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

Kudos [?]: 28 [0], given: 6

Senior Manager
Joined: 23 Jun 2009
Posts: 360

Kudos [?]: 134 [1], given: 80

Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Re: Someone please solve the PS problem in a quick way possible! [#permalink]

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22 Jul 2009, 00:54
1
KUDOS
Let say A fills in x, B fills y and C fills in z hours.
1/x + 1/y = 5/6
1/x + 1/z = 2/3
1/y+ 1/z = 1/2
Summing them
2/x + 2/y + 2/z = 12/6
1/x + 1/y + 1/z = 6/6 => They can fill 1 hours.

Kudos [?]: 134 [1], given: 80

Intern
Joined: 23 Jun 2009
Posts: 47

Kudos [?]: 28 [0], given: 6

Re: Someone please solve the PS problem in a quick way possible! [#permalink]

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22 Jul 2009, 01:00
Wow. Thanks. You're awesome!

Kudos [?]: 28 [0], given: 6

Manager
Joined: 14 Nov 2008
Posts: 195

Kudos [?]: 129 [0], given: 3

Schools: Stanford...Wait, I will come!!!
Re: Someone please solve the PS problem in a quick way possible! [#permalink]

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22 Jul 2009, 05:58
uzonwagba wrote:
I have solved it, but it took me close to 3 minutes due to long algebra. I wonder whether there is someone who could please try solving it, taking about 2 minutes, and just walk me through his/her efficient steps. Thanks.

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

take a number which is LCM of different rates.
So, let for example, the capacity is 18 Liters.
So, A+B=15 Liters/Hour
A+C=12 Liters/Hours
B+C=9 Liters/Hours.
Now adding all these 3,=> 2(A+B+C)=36
A+B+C=18
So, it will take 1 Hours for all of them together.

Kudos [?]: 129 [0], given: 3

Re: Someone please solve the PS problem in a quick way possible!   [#permalink] 22 Jul 2009, 05:58
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