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At their respective rates, pump A, B, and C can fulfill an [#permalink]
02 Apr 2009, 19:12

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A

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Difficulty:

75% (hard)

Question Stats:

51% (02:54) correct
49% (01:33) wrong based on 238 sessions

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty?

Re: PS: Pool fills [#permalink]
03 Apr 2009, 06:51

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Economist wrote:

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? A. 2/3 B. 1 C. 3/4 D. 3/2 E. 2

You can use a rates formula here, or convert each worker to the same amount of time (6 hours) :

A empties 3 tanks every 6 hours B empties 2 tanks every 6 hours C fills 1 tank every 6 hours Together, they empty 4 tanks every 6 hours So they empty 1 tank every 6/4 hours, and empty half of a tank in 3/4 hours. C. _________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Re: PS: Pool fills [#permalink]
16 Aug 2009, 11:09

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12.At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? A. 2/3 B. 1 C. 3/4 D. 3/2 E. 2

Re: PS: Pool fills [#permalink]
17 Aug 2009, 21:46

IanStewart wrote:

You can use a rates formula here, or convert each worker to the same amount of time (6 hours) :

A empties 3 tanks every 6 hours B empties 2 tanks every 6 hours C fills 1 tank every 6 hours Together, they empty 4 tanks every 6 hours So they empty 1 tank every 6/4 hours, and empty half of a tank in 3/4 hours. C.

Re: PS: Pool fills [#permalink]
17 Aug 2009, 22:17

Quote:

You can use a rates formula here, or convert each worker to the same amount of time (6 hours) :

A empties 3 tanks every 6 hours B empties 2 tanks every 6 hours C fills 1 tank every 6 hours Together, they empty 4 tanks every 6 hours So they empty 1 tank every 6/4 hours, and empty half of a tank in 3/4 hours. C.

Good job Ian. You made it all simple. _________________

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Re: PS: Pool fills [#permalink]
28 Sep 2013, 09:53

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Rate(A)=1/2 Rate(B)=1/3 Rate(C)=1/6

A + B - C

1/2 + 1/3 - 1/6 = 4/6 (Combined rate per the question)

Rate * Time = Work

4/6 * Time = 1/2

Time = 3/4 _________________

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Re: PS: Pool fills [#permalink]
17 Oct 2013, 02:53

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Expert's post

rrsnathan wrote:

TGC wrote:

Rate(A)=1/2 Rate(B)=1/3 Rate(C)=1/6

A + B - C

1/2 + 1/3 - 1/6 = 4/6 (Combined rate per the question)

Rate * Time = Work

4/6 * Time = 1/2

Time = 3/4

Hi,

I could understand this method. But my doubt is Work = Rate * time Time = Work / Rate

So as per this problem Rate(A)=1/2 Rate(B)=1/3 Rate(C)=1/6

So total time is: (1/2)/(1/2) + (1/2) / (1/3) - (1/2) / (1/6) = -1/2

Where iam missing something?? Please help me

thanks, Rrsnathan.

When adding rates you get combined rate not time. Also, why are you multiplying combined rate by 1/2?

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? A. 2/3 B. 1 C. 3/4 D. 3/2 E. 2

Rate of A = 1/2 tank/hour; Rate of B = 1/3 tank/hour; Rate of C = 1/6 tank/hour.

Combined rate when A and B are used to pump-out water, while C is used to fill water into the tank is 1/2+1/3-1/6=2/3 tank hour.

So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the half-full tank half of that time would be needed: 1/2*3/2=3/4 hours.

Work/rate problems [#permalink]
23 Nov 2013, 04:05

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? A. 2/3 B. 1 C. 3/4 D. 3/2 E. 2

Re: Work/rate problems [#permalink]
23 Nov 2013, 04:43

Expert's post

mumbijoh wrote:

At their respective rates, pump A, B, and C can fulfill an empty tank, or pump-out the full tank in 2, 3, and 6 hours. If A and B are used to pump-out water from the half-full tank, while C is used to fill water into the tank, in how many hours, the tank will be empty? A. 2/3 B. 1 C. 3/4 D. 3/2 E. 2

Merging similar topics. Please refer to the solutions above.