stevecultt wrote:A water pump began filling an empty swimming pool with water and ran at a constant rate til the swimming pool was full. At some time, the pool was 1/2 full, and 2 1/3 hours later, it was 5/6 full. How many hours would it take the pump to fill the empty pool completely?
(A) 4
(B) 5 1/3
(C) 7
(D) 7 1/5
(E) 8 1/3
Let the pool = 6 gallons.
At some time, the pool was 1/2 full, and 2 1/3 hours later, it was 5/6 full.
In 7/3 hours, the volume in the 6-gallon pool increases from 1/2 full (3 gallons) to 5/6 full (5 gallons), implying a fill rate of 2 gallons per 7/3 hours:
2/(7/3) = (2)(3/7) = 6/7 gallon per hour.
How many hours would it take the pump to fill the empty pool completely?
At a rate of 6/7 gallon per hour, the time to fill the entire 6-gallon pool = w/r = 6/(6/7) = (6)(7/6) = 7 hours.
The correct answer is
C.
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