Next-door neighbors bob and jim use hoses from both houses to fill bob's swimming pool. they know that it takes 24 h using both hoses. they also know that bob's hose, used alone, takes 20% less time than jim's hose alone. how much time is required to fill the pool by each hose alone?

fill the pool with Bob's hose: 43,2 hours and 54 hours for the Jim's hose

Explanation:

It is known that the two hoses took 24 hours to fill the pool and that Bob's hose is 20% faster than Jim's, then each hose filled a volume in 24 hours totaling the total volume of the pool. then Bob's hose takes 24 hours minus 20% to fill the volume that Jim's hose completed, that is, 24h * 0.8 = 19.2 hours, so, using Bob's hose, it would take 24h plus 19.2h = 43.2 hours to fully complete the pool. on the other hand it is known that Bob's hose is 20% faster than Jim's, so 43.2 hours will be 80% of the time it would take Jim's hose to complete the pool filling, then 43.2 * 100/80 = 54 hours it would take Jim's hose to completely fill the pool.

conservation of mass

mass before something happens = mass afterwards