Given: A certain pump working at a constant rate is used to remove rain water from a basement during a rainstorm.
Asked: If water is entering the basement at a constant rate and the pump is turned on exactly when water begins flooding the basement, is more than 1/2 of the basement flooded with water after 3 hours?
1) Water is entering the basement at a rate that is 6 times faster than the rate at which the pump is pushing water out of the basement.
Let the rate of pump pushing water out of the basement be x litres/hour
Rate of water entering the basement = 6x litres /hour
Rate of basement flooding = 5x litres/hour
Basement filled after 3 hours = 15x litres
Is 15x > 1/2 * Basement capacity in litres
Since x and basement capacity are unknown
NOT SUFFICIENT
2) After 2 hours, the basement is 2/5 flooded with water.
Since water is entering the basement at a constant rate and the pump is turned on exactly when water begins flooding the basement and after 2 hours, the basement is 2/5 flooded with water, rate of water entering the basement > rate of pump pushing water out of basement
In 2 hours, basement is 2/5 flooded with water
In 3 hours, basement will be 3/5 > 1/2 flooded with water
SUFFICIENT
IMO B
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Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com