SOLUTION: David can fill a pool in 10 hours. Working with Barney, they can fill the pool in 2 hours. How long does it take Barney to fill the pool if he works alone?

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Question 1145184: David can fill a pool in 10 hours. Working with Barney, they can fill the pool in 2 hours. How long does it take Barney to fill the pool if he works alone?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

Working together, they make    of the job per hour.


Working alone, David makes    of the job per hour.


Hence, Barney makes   -  =  =  =  of the work per hour.


It means that Barney will complete the job in   hours =  hours = 2 hours and 30 minutes.

Solved.

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It is a standard and 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 greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


An alternative solution method....

Working together, it takes them 2 hours to fill the pool.
Since it takes David 10 hours to fill the pool, in 2 hours he fills 2/10 or 1/5 of the pool.
That means Barney fills 4/5 of the pool in 2 hours; since 4/5 is 4 times as much as 1/5, Barney works 4 times as fast as David.
Since Barney works 4 times as fast as David, it will take him 1/4 as long as David to fill the pool by himself.
1/4 of 10 hours is 2.5 hours.

ANSWER: 2.5 hours
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