An inlet pipe on a swimming pool can be used to fill the pool in 30 hours. the drain pipe can be used to empty the pool in 48 hours. if the pool is 1/5 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Since both pipes are opened, you must find the net rate of inflow because some water is coming in at rate of 1/30 and some water is being drained at rate of 1/48.

Net rate = 1/30 - 1/48 = 8/240 - 5/240 = 3/240 = 1/80

This means the pool is adding water at a rate of 1/80 per hour.

To fill the pool you need 4/5 since it is starting 1/5 of the way full.
Rate*time = amount of water
1/80 * time = 4/5 pool
time = (4/5)/(1/80) = 80*(4/5) = 64

Final It will take 64 hours to fill the pool.