Pipe 1 and pipe 2 can fill a cistern in 2 and 6 hours respectively. Pipe 3 can empty the cistern in 9 hrs. If all the pipes are opened together find the time taken to fill the cistern.

Pipe 1 can fill 1/2 of the cistern in 1 hour
Pipe 2 can fill 1/6 of the cistern in 1 hour
Pipe 3 can empty 1/9 of the cistern in 1 hour
According to the question,
Time taken to full the cistern = 1/2 + 1/6 - 1/9
= 5/9
5/9 of the cistern will be filled in 1 hour.
Full cistern will be filled in = (5/9)/1
= 9/5 x 1
= 1.8 hours