Rational expressions

Question

An inlet pipe on a swimming pipe can be used to fill pool in 36 hours. The drain pipe can be used to empty the pool in 48 hours. If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

Answer 1

in one hour the inlet pipe fills 1/36 of the pool

in one hour the drain pipe empties 1/48 of the pool

in one hour together they fill (1/36-1/48) =(48-36)/(36)(48) = 12/(36)(48) = 1/3(48)= 1/144 of the pool

in x hours the two pipes together fill x(1/144) = x/144 of the pool

to fill the remaining 1/3 of the pool takes x/144 = 1/3 where x=144/3 = 48 hours