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# With both valves open, the pool will be filled with water in

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With both valves open, the pool will be filled with water in [#permalink]  02 Sep 2008, 01:23
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With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

M12-10
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Apr 2014, 23:15, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: work and time [#permalink]  02 Sep 2008, 01:58
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D. 12000 cubic meters.

If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.

Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).

or, 120x = 80 (x + 50).
or x = 100.

Hence, the capacity of pool = 120x = 12000 cubic meters.
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Re: work and time [#permalink]  02 Sep 2008, 02:14
I got the same answer (D) but used a different technique.

120x = y
48(2X+50) = Y

then, I substituted the values in the answer choices (starting with the middle then working my way in either direction) with y being the answer.

so if 120x=12000, then 48(2x+50)=12000 as well, which it does if you do the math; whereas if you use any other answer choice the two equations are not equal (do not have the same value for x and y)
this could be done much easier if you could use a graphing calculator finding the intercept of both lines, but these are not permitted in the GMAT.
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Re: work and time [#permalink]  02 Sep 2008, 03:53
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?

* 9000 cubic meters
* 10500 cubic meters
* 11750 cubic meters
* 12000 cubic meters
* 12500 cubic meters
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. What is the capacity of the pool if every minute the second valve admits 50 cubic meters of water more than the first?

Soln:
Let volume filled by first valve per minute = Va cubic meter
As first valve takes 2hours to fill the pool
therefore volume of the pool = 120 x Va....(1)

Let the volume filled by second valve per minute = Vb cubic meter

Total volume filled by both the valves in 48 minutes = Va x 48 + Vb x 48
According to the condition of the problem

Vb = Va + 50

therefore total vulme filled in 48 minutes
Va x 48 + (Va+50) x 48 = volume of the pool = 120 Va ..from (1)
or, Va = 100

Total volume of the pool = 100 x 120 = 12000 cubic meters

Option D
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Last edited by hksingh83 on 02 Sep 2008, 04:07, edited 1 time in total.
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Re: work and time [#permalink]  02 Sep 2008, 04:02
This one took me ages to solve.

1/48 = 1/120 + x --> solve for x. x = 1/80
y(1/80) = y(1/120) + 50 --> y = 12,000
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Re: With both valves open, the pool will be filled with water in [#permalink]  22 Apr 2014, 21:31
Let 1st does in 1 minute =x so, in 120 min= 120x
2nd does=x+50
A/Q, 48x+48(x+50)=120x
X= 100
120x= 12000 (D)
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Re: With both valves open, the pool will be filled with water in [#permalink]  22 Apr 2014, 23:15
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arjtryarjtry wrote:
With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity of the pool?

A. 9000 cubic meters
B. 10500 cubic meters
C. 11750 cubic meters
D. 12000 cubic meters
E. 12500 cubic meters

M12-10

Let the rate of the first valve be $$x$$ cubic meters per minute, then the rate of the second valve will be $$x+50$$ cubic meters per minute.

As both valves open fill the pool in 48 minutes then the capacity of the pool equals to $$C=time*combined \ rate=48(x+x+50)=48(2x+50)$$;
But as the first valve alone fills the pool in 2 hours (120 minutes) then the capacity of the pool also equals to $$C=time*rate=120x$$;

So, $$120x=48(2x+50)$$ --> $$x=100$$ --> $$C=120x=12,000$$.

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Re: With both valves open, the pool will be filled with water in [#permalink]  23 Apr 2015, 18:01
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Re: With both valves open, the pool will be filled with water in   [#permalink] 23 Apr 2015, 18:01
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