A swimming pool holds 10,000 gallons of water. It can be filled at the rate of 1

Question

A swimming pool holds 10,000 gallons of water. It can be filled at the rate of 100 gal/min and emptied at the same rate. Right now, the pool is filled, but there are 20 pounds of an impurity dissolved in the water. For the safety of the swimmers, this must be reduced to less than 1 pound. It would take 200 minutes to empty the pool completely and refill it, but during part of this time the pool could not be used. How long will it take to restore the pool to a safe condition if at all times the pool must be at least half full?

answer = 165.12 minutes. Please show method.

Explanation / Answer

Swimming pool holds 10,000 gallons of water,

it filled at 100gla/mina and 200 min take to fill it

so totally swimming pool can hold have 100*200=20,000

so that 20 pounds of an impurity dissolved in the water. For the safety of the swimmers, this must be reduced to less than 1 pound.

And it take 200 minutes to empty the pool completely and refill it.

but now at all times the pool must be at least half full:200/2 to 200

                                                                               100 to 200 minuits take.

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