SOLUTION: if barbara were to paint her room alone, it would take 4 hours. her sister Sarah could do the job in 5 hours. How long would it take them working together?

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Question 1149556: if barbara were to paint her room alone, it would take 4 hours. her sister Sarah could do the job in 5 hours. How long would it take them working together?
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
if barbara were to paint her room alone, it would take 4 hours. her sister Sarah could do the job in 5 hours. How long would it take them working together?
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Probably 20 hours as they would start giggling instead of working.

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

Barbara makes  1%2F4  of the job per hour.


Sarah   makes  1%2F5  of the job per hour.


Workin together, the sisters make  1%2F4 + 1%2F5 = 5%2F20 + 4%2F20 = 9%2F20 of the job per hour.


It means, that the can complete the job in  20%2F9 = 22%2F9 hours, working together.

Solved.


This method requires making manipulations with fractions, only.
It does not require solving equation.

If you want or if you need to solve it using equation/equations, do it as follows. 


Let "t" be the time for two to complete the job, in hours.


Barbara makes  1%2F4  of the job per hour --- hence, she will make  t%2F4  of the job in "t" hours.


Sarah makes  1%2F5  of the job per hour --- hence, she will make  t%2F5  of the job in "t" hours.


Since they completes the entire work in t hours,

    t%2F4 + t%2F5 = 1.


Multiply both sides by 4*5. You will get

    5t + 4t = 20,

    9t      = 20

     t      = 20%2F9  hours,   the same ANSWER

Now you know two basic ways to solve this problem.

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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.