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

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nhai2003: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Tue Feb 10, 2009 11:30 pm

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

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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Source: Beat The GMAT — Problem Solving | Mon Jul 13, 2009 7:16 pm

zenithexe: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Tue Jun 16, 2009 8:20 pm; Thanked: 5 times

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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mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 am; Location: Sydney; Thanked: 23 times; Followed by:1 members

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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tom4lax: Master | Next Rank: 500 Posts; Posts: 175; Joined: Mon Feb 09, 2009 3:57 pm; Thanked: 4 times

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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doclkk: Master | Next Rank: 500 Posts; Posts: 180; Joined: Tue Apr 07, 2009 3:46 pm; Thanked: 5 times; Followed by:2 members

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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 Â½ 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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