alandizzle wrote:
Working alone at its constant rate, pump x pumped out 1/3 of the water in a pool in 4 hours. Then pump Y started working and the two pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 6 hours. How many hours would it have taken pump Y, working alone at its constant rate, to pump out all the water that was pumped out of the pool?
A: 18
B: 24
C: 36
D: 48
E: 52
We are given that pump X pumped out 1/3 of the water in a pool in 4 hours. Since rate = work/time, the rate of pump X is (1/3)/4 = 1/12. Also, since 1/3 of the water was pumped out of the pool, 2/3 was left to be removed.
Since pump X and Y pumped out 2/3 of the water in 6 hours, the combined rate of pumps X and Y is (2/3)/6 = 2/18 = 1/9.
Finally, since rate of pump X + rate of pump Y = the combined rate of pumps X and Y, the rate of pump Y is:
1/9 - 1/12 = 4/36 - 3/36 = 1/36
Thus, pump Y can pump all the water out of the pool in 36 hours.
Answer: C
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