Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know that it takes 12 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?

Jim's hose: 27 hours.

Bob's hose: 21.6 hours.

Step-by-step explanation:

Let t represent hours taken by Jim's hose.

Part of pool filled by Jim's hose in 1 hour would be .

We have been given that Bob's hose, used alone, takes 20% less time than Jim's hose alone. This means that Bob's hose take will take 80% time of Jim's hose that is .

Part of pool filled by Bob's hose in 1 hour would be .

We are also told that it takes 12 hours using both hoses. Part of pool filled by both hoses in 1 hour would be .

Now, we will add rates of both hoses and equate with as:

Cross multiply:

Therefore, it will take 27 hours for Jim's hose to fill the pool alone.

Time take by Jim's hose alone: .

Therefore, it will take 21.6 hours for Bob's hose to fill the pool alone.