Question 279509
An inlet pipe on a swimming pool can be used to fill the pool in 23 hours. The drain pipe can be used to empty the pool in 24 hours. If the pool is 1/4 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?

the inlet does 1/23 of the job in 1 hour

the drainpipe does 1/24 job in 1 hour

Effectively if both are open then 1/23 - 1/24 job is done in 1 hour

1/ 23*24 job will be done in 1 hour

the pool is 1/4 full so 3/4 empty. So to complete 3/4 of the job it will take

(3/4) /  (1/ 23*24)  

= 414 hours