# Thread: Help with hoses please!

1. ## Help with hoses please!

Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 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?

I came up with 9h and 11h. Please help!

2. Originally Posted by pochoa
Next-door neighbors Bob and Jim use hoses from both houses to fill Bob's swimming pool. They know it takes 18 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?

I came up with 9h and 11h. Please help!
Hello,

I'm very sorry, but your answer couldn't be right because one hose needs a lot more time to fill the swimmingpool than both hoses together.

Let's have another try:

(I use SP as abbreviation for "swimmingpool")

Bob's hose needs b hours to fill the SP.
Jim's hose needs j hours to fill the SP.
That means:
Bob's hose delivers $\frac{SP}{b}$ per hour.
Jim's hose delivers $\frac{SP}{j}$ per hour.
Both hoses together delivers $\frac{SP}{b}+\frac{SP}{j}$ per hour.
They need 18 hours to fill the SP:
$18 \cdot \left( \frac{SP}{b}+\frac{SP}{j} \right)=SP$
Expanded:
$\frac{18 \cdot SP}{b}+\frac{18 \cdot SP}{j} =SP$
Divide both sides of the equation by SP and you get:
$\frac{18}{b}+\frac{18}{j} =1$

As we know that $b=0.8 \cdot j$ we can substitute b by j:
$\frac{18}{0.8 \cdot j}+\frac{18}{j} =1$

I leave the next steps to you.

As the final result you'll get b=32.4 hrs (32 h; 24 min) and j = 40.5 hrs (40 h; 30 min).

Bye

,

### next door neighbours bob and jim houses from both houses to fill bob's swimming pool.then know that bob's house , used alone takes 70% less time than jim house alone how much time is required to fill the pool

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