alanforde800Maximus wrote:At a community center, three separate pumps- A, B, and C- started to fill an empty swimming pool at 8:00 AM, and each pump worked at its own constant rate until the pool was full. Was the pool completely filled at 3:00 PM?
1) Working alone, pump C could fill 3/10 of the pool in 126 minutes.
2) Working together, pumps A and B could fill 1/8 of the pool in 55 minutes.
Please assist with above problem.
8am - 3pm = 7 hours = 420 minutes.
Statement 1:
Let the pool = 10 liters, implying that 3/10 of the pool = (3/10)(10) = 3 liters.
Since C can pump 3 liters in 126 minutes, C's rate = w/t = 3/126 = 1/42 liters per minute.
Amount pumped by C in the 420 minutes between 8am and 3pm = rt = (1/42)(420) = 10 liters.
Thus, the 10-liter pool will be filled by 3pm.
SUFFICIENT.
Statement 2:
Let the pool = 8 liters, implying that 1/8 of the pool = (1/8)(8) = 1 liter.
Since A and B together can pump 1 liter in 55 minutes, the combined rate for A and B = w/t = 1/55 liters per minute.
Amount pumped by A and B in the 420 minutes between 8am and 3pm = rt = (1/55)(420) = 84/11 = less than 8 liters.
Thus, A and B alone cannot fill the 8-liter pool by 3pm.
Since C's rate is unknown, it is not possible to determine whether the pool will be filled by 3pm.
INSUFFICIENT.
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