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At their respective rates, pump A, B, and C can fulfill an [#permalink]

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02 Apr 2009, 20:12

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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?

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.
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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

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.

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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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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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.

Re: At their respective rates, pump A, B, and C can fulfill an [#permalink]

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18 Apr 2015, 13:57

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Re: At their respective rates, pump A, B, and C can fulfill an [#permalink]

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21 Sep 2015, 03:16

Time required to half the tank by each = (time for full tank)/2 Therefore A=1hour B=3/2 hour C=6/2 hour Now A and B empties and C adds => 1/A + 1/B - 1/C = 1+2/3-2/6 =8/6=4/3 hence 3/4 ans

Re: At their respective rates, pump A, B, and C can fulfill an [#permalink]

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13 Oct 2015, 06:19

Bunuel wrote:

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.

Answer: C.

Hope it's clear.

how did the reciprocal come. I mean 2/3 tank per hour into 3/2 I did not get that logic

At their respective rates, pump A, B, and C can fulfill an [#permalink]

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25 Nov 2015, 11:17

Let’s say work = 12 then: Rate A = 6 Rate B = 4 Rate C = 2 There combined rate \(= 6+4-2=8\) and 50% of the tank \(=\frac{12}{2}=6\), \(hence 8*t=6, \frac{t=3}{4}\) Answer C
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Re: At their respective rates, pump A, B, and C can fulfill an [#permalink]

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25 Nov 2015, 12:00

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

Let the volume of the tank be 12 units

Efficiency of tank A = -6 { -ve since they are pumpung out water} Efficiency of tank B = -4 { -ve since they are pumpung out water} Efficiency of tank C = 2

We are given the information that the tank is half filled, so 6 units is filled

Net/Effective work done by the 3 pipes is (-6)+ (-4) +(2) =>-8 units

So, the three pipes will drain out water and the time required to do the same from the half filled tank is 6/8 => 3/4

Answer is (C)

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Re: At their respective rates, pump A, B, and C can fulfill an [#permalink]

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06 Dec 2015, 12:40

lets set the equation as: water in the tank + water pump in = water pump out

This will give you the following: 1/2 + 1/6(T) = (1/2)T + (1/3)T where T is the required time so that the tank is empty solve for T, you will get T = 3/4 hr

so the answer is C

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Re: At their respective rates, pump A, B, and C can fulfill an
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06 Dec 2015, 12:40

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