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At their respective rates, pump A, B, and C can fulfill an
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Updated on: 29 Sep 2013, 09:37
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At their respective rates, pump A, B, and C can fulfill an empty tank, or pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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
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Originally posted by Economist on 02 Apr 2009, 20:12.
Last edited by Bunuel on 29 Sep 2013, 09:37, edited 1 time in total.
Renamed the topic and edited the question.




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Re: PS: Pool fills
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03 Apr 2009, 07:51
Economist wrote: At their respective rates, pump A, B, and C can fulfill an empty tank, or pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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 hoursTogether, 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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Re: PS: Pool fills
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28 Sep 2013, 10:53
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
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16 Aug 2009, 12:09
12.At their respective rates, pump A, B, and C can fulfill an empty tank, or pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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 X = # of hours for the tank to empty
X*Rate A + X*Rate B  X*Rate C = 1/2 tank
X*(1/2) + X*(1/3)  X*(1/6) = 1/2 X = 3/4
It takes 3/4 hrs to empty the tank
ANSWER: C. 3/4



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Re: PS: Pool fills
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24 Aug 2009, 23:30
Effective rate(empty) : 1/2+1/31/6 = 4/6 = 2/3
So whole tank will be emptied in 3/2 hrs..and half will be in 3/4 hrs. C...



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Re: PS: Pool fills
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17 Oct 2013, 03:53
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) = 1/2Where 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 pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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 pumpout water, while C is used to fill water into the tank is 1/2+1/31/6=2/3 tank hour. So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the halffull tank half of that time would be needed: 1/2*3/2=3/4 hours. Answer: C. Hope it's clear.
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Re: At their respective rates, pump A, B, and C can fulfill an
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04 Apr 2014, 02:16
Effective rate of A, B & C respectively \(= \frac{1}{2} + \frac{1}{3}  \frac{1}{6}\) (ve as tank is getting empty) \(= \frac{3+21}{6}\) \(= \frac{4}{6}\) \(= \frac{2}{3}\) Time required for full tank \(= \frac{3}{2}\) \(Time required for half tank = \frac{3}{2} * \frac{1}{2} = \frac{3}{4}\) Answer = C
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Re: PS: Pool fills
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17 Aug 2009, 22:46
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. that looks so simple and easy.. thanks Ian.



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Re: PS: Pool fills
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17 Aug 2009, 23:17
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
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12 Oct 2013, 00:14
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.



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Re: At their respective rates, pump A, B, and C can fulfill an
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26 Oct 2013, 10:08
t*[C's rate  (A's rate+B's rate)] + current tank size = 0 t*[1/6  (1/2+1/3)] + .5 = 0 t = 3/4



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Re: At their respective rates, pump A, B, and C can fulfill an
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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+2/32/6 =8/6=4/3 hence 3/4 ans



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Re: At their respective rates, pump A, B, and C can fulfill an
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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) = 1/2Where 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 pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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 pumpout water, while C is used to fill water into the tank is 1/2+1/31/6=2/3 tank hour. So, to empty the full tank 3/2 hours (reciprocal of rate) are needed. To empty the halffull 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



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At their respective rates, pump A, B, and C can fulfill an
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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 \(= 6+42=8\) 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
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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 pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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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At their respective rates, pump A, B, and C can fulfill an
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25 Nov 2015, 18:16
t=time to empty tank t(1/65/6)=1/2➡t(2/3)=1/2 t=3/4 hour



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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
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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28 Mar 2018, 10:35
Economist wrote: At their respective rates, pump A, B, and C can fulfill an empty tank, or pumpout the full tank in 2, 3, and 6 hours. If A and B are used to pumpout water from the halffull 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 We can calculate the net outflow rate (i.e., the sum of the rates of A and B minus the rate of C) as: 1/2 + 1/3  1/6 = 3/6 + 2/6  1/6 = 4/6 = 2/3 Since only ½ of a tank needs to be emptied, the time it takes to do that is (1/2)/(2/3) = 1/2 x 3/2 = 3/4 hour. Answer: C
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