SOLUTION: Working together, Jessica and Jill can install a new deck in 9 hours. Had she done it alone it would have taken Jill 21 hours. How long would it take Jessica to do it alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Working together, Jessica and Jill can install a new deck in 9 hours. Had she done it alone it would have taken Jill 21 hours. How long would it take Jessica to do it alone?      Log On


   



Question 1180590: Working together, Jessica and Jill can install a new deck in 9 hours. Had she done it alone it would have taken Jill 21 hours.
How long would it take Jessica to do it alone?

Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
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Working together, Jessica and Jill can install a new deck in 9 hours.
Had she done it alone it would have taken Jill 21 hours.
How long would it take Jessica to do it alone?
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Their combined rate of work is  1%2F9  of the job per hour.


Jill's individual rate of work is  1%2F21  of the job per hour.


Hence, Jessica's individual rate of work is the difference


    1%2F9 - 1%2F21 = 21%2F%289%2A21%29 - 9%2F%289%2A21%29 = %2821-9%29%2F%289%2A21%29 = 12%2F%289%2A21%29 = 4%2F%283%2A21%29 = 4%2F63


of the job per hour.


It means that Jessica can complete the job in  63%2F4 = 15 3%2F4  hours = 15 hours and 45 minutes.    ANSWER

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.