a pool takes six hours to fill and eight hours to drain. The drain was accidently left open for the first three hours while the pool was filling and then closed. How long did it take for the pool to be filled?

Answer 1

fill rate = 1/6 pool/hr
drain rate = 1/8 pool per hour

rate with both = 1/6 -1/8 = 4/24 -3/24
= 1/24 pool/hour
so in three hours
(1/24 pool/hr )* 3 hr = 1/8 pool filled in first three hours
so we still need to fill 7/8 of pool
(1/6 pool/hr)* x hr = 7/8 pool
x = 42/8 hours to finish
so
3 + 42/8 = 8 1/4 hours total