SOLUTION: 10. One hose can fill a swimming pool in 40 hours while the second hose fills the pool in 60 hours. How long would it take to fill-up the swimming pool using both hoses together?

Question 1102270: 10. One hose can fill a swimming pool in 40 hours while the second hose fills the pool in 60 hours. How long would it take to fill-up the swimming pool using both hoses together?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.

First hose fills of the pool volume each hour. Second hose fills of the pool volume each hour. Working together, they fill + = = = of the pool volume per hour. Hence, it will take 24 hours to fill the pool using both hoses together.

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It is a typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
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    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

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The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

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https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

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Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Combined Rate,

Time for both hoses combined, 24 hours
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Here is an alternative method for solving these "working together" problems that I find many students prefer to the standard algebraic method shown by the other tutors.

One hose takes 40 hours to fill the pool alone; another takes 60 hours.
Imagine you have several of these pools.
The least common multiple of 40 and 60 is 120.
In 120 hours the first hose could fill 3 pools and the second hose could fill 2 pools.
So in 120 hours the two hoses together could fill 5 pools.
But at that rate the two together could fill the one pool in 120/5 = 24 hours.
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