Answer:
22.5 hours
Step-by-step explanation:
I am using "1 pond" to mean the volume of water that fits in the pond.
The inlet pipe fills the pond in 9 hours.
The filling rate is (1 pond)/(9 hours) = 1/9 pond/hour
The outlet pipe empties the pond in 15 hours.
The emptying rate is (1 pond)/(15 hours) = 1/15 pond per hour
The difference in rates is the net rate at which the pond is filling up.
1/9 pond/hour - 1/15 pond/hour =
= 5/45 pond/hour - 3/45 pond /hour
= 2/45 pond/hour
The pond is filling at a rate of 2/45 pond/hour.
To find the time it takes to fill the pond, we divide 1 pond by the rate.
(1 pond)/(2/45 pond/hour) = 45/2 hour = 22.5 hours
