enigma123
An empty swimming pool with a capacity of 75,000 liters is to be filled by hoses X and Y simultaneously. If the amount of water flowing from each hose is independent of the amount flowing from the other hose, how long, in hours, will it take to fill the pool?
(1) If hose X stopped filling the pool after hoses X and Y had filled half the pool, it would take 21 hours to fill the pool.
(2) If hose Y stopped filling the pool after hoses X and Y had filled half the pool, it would take 16 hours to fill the pool.
Statement 1:When X and Y together fill half the pool and Y alone fills the remaining half, the total time = 21 hours.
Implication:
If X and Y together fill the ENTIRE pool, the time will be LESS than 21 hours.
No way to determine the exact time.
INSUFFICIENT.
Statement 2:When X and Y together fill half the pool and X alone fills the remaining half, the total time = 16 hours.
Implication:
If X and Y together fill the ENTIRE pool, the time will be LESS than 16 hours.
No way to determine the exact time.
INSUFFICIENT.
Statements combined:Since half the pool = 37,500 liters, it is almost certain that the 21-hour time in Statement 1 is split between two times that divide evenly into 37,500.
Since 37,500 is divisible by 6 and 15, test a time of 6 hours for X and Y together to fill the first half of the pool and a time of 15 hours for Y alone to fill the remaining half, for a total time of 21 hours.
If X and Y together take 6 hours to pump in the first 37,500 liters, the rate for X and Y together = \(\frac{work}{time} = \frac{37,500}{6} = 6250\) liters per hour.
If Y takes 15 hours to pump in the remaining 37,500 liters, the rate for Y alone \(= \frac{work}{time} = \frac{37,500}{15} = 2500\) liters per hour.
Resulting rate for X alone = (rate for X and Y together) - (Y's rate alone) = 6250-2500 = 3750 liters per hour.
Do the values above satisfy Statement 2, which indicates a total time of 16 hours when X and Y fill half the pool and X alone fills the remaining half?
If X and Y together take 6 hours to fill the first half of the pool, the time for X alone -- working at a rate of 3750 liters per hour -- to fill the remaining half of the pool \(= \frac{work}{rate} = \frac{37,500}{3750} = 10\) hours, for a total time of 16 hours.
Statement 2 is satisfied.
Since the tested values satisfy both statements, we know that the time for X and Y together to fill half the pool = 6 hours, implying a total time of 12 hours for X and Y to fill the entire pool.
SUFFICIENT.