Two Pipes filling a Pool

Question

When two pipes fill a pool together, they can finish in 5 hours. If one of the pipes fills half the pool then the other takes over and finishes filling the pool, it will take them 18 hours. How long will it take each pipe to fill the pool if it were working alone?

Answer 1

This is a pretty good problem, I enjoyed to solve one.

Answer: The fastest pipe - 6 hours

The slowest pipe - 30 hours.

Notice, that you cannot say which one is faster and which one is slower, first pipe or second pipe. I will show my work if you show us what have you tried. Otherwise it is useless.