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At their respective rates, pump A, B, and C

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by nhai2003 » Mon Jul 13, 2009 7:16 pm
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

Please help!
[spoiler]OA: C[/spoiler]
Last edited by nhai2003 on Mon Jul 13, 2009 10:14 pm, edited 1 time in total.
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by zenithexe » Mon Jul 13, 2009 9:11 pm
IMO C[spoiler]
Let speed at which pumps fill/pump out be A,B,C for each pump A,B,C receptively.

Since pump A can pump-out/fill full tank in 2hours, A=T/2hours, where is is volume of tank. (this is just application of V=D/T velocity calculations)

and B=T/3, C=T/6

Since tank is half full, this can be noted as T*0.5

the answer=0.5T/(A+B-C) since A,B,C is speed at which pumps operate, C must be subtracted from A+B as it is working against them

substitute and solve

=0.5T/(A+B-C)
=0.5T/(T/2+T/3-T/6)
=0.5T/((3T+2T-T)/6)
=3T/4T
=3/4[/spoiler]

I hope I'm right XP
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by mehravikas » Mon Jul 13, 2009 9:18 pm
Is it C?

A full tank will be emptied in 3/2 hrs -> 1/6 - (1/2 + 1/3)

If the tank is half full it should half the time of 3/2 hours i.e. 3/4 hrs
Last edited by mehravikas on Wed Jul 15, 2009 12:24 pm, edited 1 time in total.
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by tom4lax » Tue Jul 14, 2009 5:15 am
I also got C, but used a slightly different approach:

Pumps A & B empty the tank at (1/2 + 1/3) or at a rate of 5/6. Pump C operates in the opposite direction of 1/6, so total for all 3 pumps is 4/6.

4/6 x T = 1/2

T = 3/4
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by doclkk » Tue Jul 14, 2009 3:59 pm
tom4lax wrote:I also got C, but used a slightly different approach:

Pumps A & B empty the tank at (1/2 + 1/3) or at a rate of 5/6. Pump C operates in the opposite direction of 1/6, so total for all 3 pumps is 4/6.

4/6 x T = 1/2

T = 3/4
I liked this method a lot.
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by Scott@TargetTestPrep » Wed Mar 28, 2018 9:38 am
nhai2003 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
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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