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?

Algebra ->  Percentage-and-ratio-word-problems -> 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?      Log On


   

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) About Me  (Show Source):
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.
First hose fills 1%2F40 of the pool volume each hour.


Second hose fills 1%2F60 of the pool volume each hour.


Working together, they fill 1%2F40 + 1%2F60 = 3%2F120+%2B+2%2F120 = 5%2F120 = 1%2F24 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
    - Using Fractions to solve word problems on joint work
    - 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.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

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


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Combined Rate, 1%2F40%2B1%2F60

%2860%2B40%29%2F%2840%2A60%29

100%2F2400

1%2F24

Time for both hoses combined, 24 hours

Answer by greenestamps(13200) About Me  (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.