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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