A pump started filling an empty pool with water and continued at a constant rate until the pool was full. At noon the pool was 1/3 full, and 1 + 1/4 hours later it was 3/4 full. What was the total number of hours that it took the pump to fill the pool?
A. 2 + 1/3
B. 2 + 2/3
C. 3
D. 3 + 1/2
E. 3 + 2/3
Let the capacity of the pool = 12 gallons.
Since the pool is 1/3 full at noon, the amount in the pool at noon = (1/3)(12) = 4 gallons.
Since the pool is 3/4 full 1.25 hours later, the amount in the pool 1.25 hours later = (3/4)(12) = 9 gallons.
Since in 1.25 hours the pump increases the volume from 4 to 9 gallons -- for a total increase of 5 gallons -- the pump's rate = w/t = 5/1.25 = 500/125 = 4 gallons per hour.
Since the pump's rate = 4 gallons per hour, the total time for the pump to fill the 12-gallon pool = w/r = 12/4 = 3 hours.
The correct answer is
C.
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