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Marge has 3 pumps for filling her swimming pool. When all 3

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Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink] New post 10 Feb 2013, 06:11
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Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?

A) 2hrs, 48mins
B) 6hrs, 32mins
C) 7hrs, 12mins
D) 13hrs, 4mins
E) 14hrs, 24mins
[Reveal] Spoiler: OA

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink] New post 10 Feb 2013, 06:32
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Rock750 wrote:
Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?

A) 2hrs, 48mins
B) 6hrs, 32mins
C) 7hrs, 12mins
D) 13hrs, 4mins
E) 14hrs, 24mins


The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.

Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes = 6 hours and 32 minutes.

Answer: B.

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink] New post 10 Feb 2013, 06:35
Rock750 wrote:
Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 3 at its maximum rate ?

A) 2hrs, 48mins
B) 6hrs, 32mins
C) 7hrs, 12mins
D) 13hrs, 4mins
E) 14hrs, 24mins


I'll use letters to label the pumps rather than numbers, because there will be so many numbers elsewhere in the solution. Real GMAT questions would normally compare how long it takes each pump to fill the pool, rather than compare the rates at which each pump fills the pool. That is, a real GMAT question would say that Pump C takes four times as long as Pump A (if A's rate is four times that of C, then C takes four times as long), and that Pump B takes twice as long as Pump A.

So, say Pump A fills the pool in t minutes. Then we know:

A fills 1 pool in t minutes
B fills 1 pool in 2t minutes
C fills 1 pool in 4t minutes

You could use the rates formula now, or you can just get the same amount of time for each pump - we can use 4t minutes:

A fills 4 pools in 4t minutes
B fills 2 pools in 4t minutes
C fills 1 pool in 4t minutes

So if they all work together for 4t minutes, they fill 4+2+1 = 7 pools. If they fill 7 pools in 4t minutes, they fill 1 pool in 4t/7 minutes. This is equal to 56 minutes, from the question, so

4t/7 = 56
4t = 56*7
4t = 392

Notice that 4t is what we wanted to find - that's the time it takes pump C. So the answer is 392 minutes, or 6 hours and 32 minutes.

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink] New post 03 Jun 2013, 23:06
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My approach is quite similar to Bunuel's.
A,B,C - each pump's rate respectively. We know that all 3 pumps fill the pool for 56 min:
1/(A+B+C)=56
We also know that:
A=2B=4C; or A= 4C and B=2C

substitute these equalities in first equation:
1/(4C+2C+C)=56 ====> 1/7C=56 ===> C=1/392 meaning that pump C needs 392 minutes or 6 h 32 min to fill the pool alone.
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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink] New post 05 Jun 2013, 09:01
I think of the fraction of the pool that each pump fills.
If the third pump fills up x, the second pump fills up 2x, and the first pump fills up 4x, so there are seven "parts" (4+2+1)
which means
First pump fills 4/7 of the pool in 56 mins
2nd pump fills 2/7 of the pool in 56 mins
3rd pump fills 1/7 of the pool in 56 mins

for the 3rd pump to fill the whole pool by itself, it would take 7 times the time. So...
56 x 7 = 392 mins = 6 hours and 32 minutes

Answer is B
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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink] New post 19 Jun 2013, 04:36
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I am getting the same solution like Bunuel
Using the method of The Highest Common Factor
Given that x+2x+4x=1/56
x=1/392
= 392 minutes
= 6 hours and 32 minutes.
Re: Marge has 3 pumps for filling her swimming pool. When all 3   [#permalink] 19 Jun 2013, 04:36
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