Marge has 3 pumps for filling her swimming pool. When all 3 : GMAT Problem Solving (PS)
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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]

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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]

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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.

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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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]

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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.
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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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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]

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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

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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26 Oct 2014, 04:28
1/x+1/2x+1/4x=1/56
7/4x=1/56
x=1/98 portion of work per minute does fastest pump.
So, slowest does 1/98*4=1/392 portion, i.e in 392 min.
392/60=6.5... or 6h.32 min

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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01 Oct 2016, 17:40
Bunuel wrote:
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.

Water pumped by pump 1 in 56 mins : 400 lts
Water pumped by pump 2 in 56 mins : 200 lts
Water pumped by pump 3 in 56 mins : 100 lts

total water pumped in 56 mins by all: 700 lts

Hence, pump 3 needs to pump 700 lts

for pump 3,

100 lts take 56 mins
so 700 lts will take 56 * 7 = 350 + 42 = 392mins = 392/60 hours = 6 hours and 32 mins.
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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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09 Nov 2016, 23:41
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

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Re: Marge has 3 pumps for filling her swimming pool. When all 3 [#permalink]

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10 Nov 2016, 09:31
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

Ratio of efficiency of the 3 pumps is -

Pump - I : Pump - II : Pump - III = 4 : 2 : 1

Total capacity is 56*7

Time taken to fill the tank using only Pump - III = $$\frac{56*7}{60}$$ = 6 Hrs 32 minutes...

Hence, Answer will be (B) 6hrs, 32mins
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Re: Marge has 3 pumps for filling her swimming pool. When all 3   [#permalink] 10 Nov 2016, 09:31
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