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A drain pump can remove water from a storage tank at a constant rate of \(n\) liters per hour, while an inlet valve can add water to the tank at a constant rate of \(m\) liters per hour, where \(n > m\). If both start operating at the same time when the tank contains exactly 168 liters of water, how many hours will it take for the tank to become empty?
(1) \(n - m = 24\)
(2) After 3 hours of both operating, the tank contains 96 liters of water.
(1) \(n - m = 24\)
(2) After 3 hours of both operating, the tank contains 96 liters of water.
30 May 2026, 09:01
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Official Solution:
A drain pump can remove water from a storage tank at a constant rate of \(n\) liters per hour, while an inlet valve can add water to the tank at a constant rate of \(m\) liters per hour, where \(n > m\). If both start operating at the same time when the tank contains exactly 168 liters of water, how many hours will it take for the tank to become empty?
Time to empty the tank = \(\frac{168}{n - m}\).
(1) \(n - m = 24\)
So time = \(\frac{168}{24} = 7\) hours. Sufficient.
(2) After 3 hours of both operating, the tank contains 96 liters of water.
In 3 hours, the tank goes from 168 to 96, a drop of 72 liters. So the net draining rate is \(\frac{72}{3} = 24\) liters per hour, meaning \(n - m = 24\). Then time = \(\frac{168}{24} = 7\) hours. Sufficient.
Answer: D
A drain pump can remove water from a storage tank at a constant rate of \(n\) liters per hour, while an inlet valve can add water to the tank at a constant rate of \(m\) liters per hour, where \(n > m\). If both start operating at the same time when the tank contains exactly 168 liters of water, how many hours will it take for the tank to become empty?
Time to empty the tank = \(\frac{168}{n - m}\).
(1) \(n - m = 24\)
So time = \(\frac{168}{24} = 7\) hours. Sufficient.
(2) After 3 hours of both operating, the tank contains 96 liters of water.
In 3 hours, the tank goes from 168 to 96, a drop of 72 liters. So the net draining rate is \(\frac{72}{3} = 24\) liters per hour, meaning \(n - m = 24\). Then time = \(\frac{168}{24} = 7\) hours. Sufficient.
Answer: D
