Question

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?

Answer 1

Answer:

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 $\frac{1}{t}$.

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 $0.8t$.

Part of pool filled by Bob's hose in 1 hour would be $\frac{1}{0.8t}$.

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

Now, we will add rates of both hoses and equate with $\frac{1}{12}$ as:

$\frac{1}{t}+\frac{1}{0.8t}=\frac{1}{12}$

$\frac{0.8}{0.8t}+\frac{1}{0.8t}=\frac{1}{12}$

$\frac{0.8+1}{0.8t}=\frac{1}{12}$

$\frac{1.8}{0.8t}=\frac{1}{12}$

Cross multiply:

$0.8t*1=1.8(12)$

$0.8t=21.6$

$\frac{0.8t}{0.8}=\frac{21.6}{0.8}$

$t=27$

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

Time take by Jim's hose alone: $0.8t\Rightarrow 0.8(27)=21.6$.

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