A pool can be filled in 4 hours and drained in 5 hours. The valve that fills the pool was opened at 1pm and some time alter the drain that empties the pool was also opened. If the pool was filled by 11pm and not earlier, when was the drain opened?
Let Pool = 20
Filled at the rate of: 20/4 = 5 pool/hr
Drained at the rate of: 20/5 = 4 pool/hr
When both valves are open, the pool is filled at the rate of: 5-4 = 1 pool/hr
Let x be the amount that is filled when only filling valve is open.
Therefore, 20-x is the amount that is filled when both valves are open.
Total time to fill the pool = 10 hrs
x/5 + (20-x)/1 = 10 --> (time taken when only filling valve is open = x/5; time taken when both valves are open = 20-x)
x = 12.5 --> (this is the amt. of pool filled when only the filling valve is open, i.e., when the draining valve is shut)
x/5 = 12.5/5 = 2.5 hrs --> (this is the duration for which only the filling valve was open)
Therefore, the draining valve was opened at 1 pm + 2.5 hrs = 3:30 pm