Carcass wrote:
Olga’s swimming pool has three pipes connected to it. If the pool is empty, pipe A can fill it in 3 hours and pipe B can fill it in 4 hours. If the pool is at capacity, pipe C can empty it in 2 hours. The capacity of Olga’s pool is 2,400 cubic meters. If all three pipes are activated when the pool is empty, how many hours will it take for the pool to be filled to 60 percent of capacity?
A. 7.0
B. 7.2
C. 8.0
D. 8.6
E. 12.0
KUDOS for the right solution and explanation
*** If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours , then on opening both the pipes,
the net part filled in 1 hour = \({\frac{1}{x} - \frac{1}{y} }\) .
Here,
First calculate, how much time it would take to fill the tank to full capacity
We know,
Work = Rate * Time
1 = \((\frac{1}{3} + \frac{1}{4 }- \frac{1}{2})\)
* Timeor Time taken to fill the tank =
12 hours
Now, in 12 hours with pipes A, B and C open it can fill
2400 cubic metersTherefore, to fill up 60% i.e
1440 cubic meters, as per given criteria, it will take = \(\frac{12}{2400} * 1440 = 7.2\) hours
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