SOLUTION: Christina can paint a chair in 3 ​hours, and Victoria can paint a chair in 5 hours. How many hours will it take to paint the chair when the two girls work​ together? Write an e

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Christina can paint a chair in 3 ​hours, and Victoria can paint a chair in 5 hours. How many hours will it take to paint the chair when the two girls work​ together? Write an e      Log On


   



Question 1142678: Christina can paint a chair in 3 ​hours, and Victoria can paint a chair in 5 hours. How many hours will it take to paint the chair when the two girls work​ together? Write an equation that could be used to model this problem. Let t represent the time​ (in hours) that it will take to paint the chair when the two girls work together
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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Since Christina can make the entire job in 3 hours, working alone, she makes  1%2F3  of the job per hour.


Since Victoria can make the entire job in 5 hours, working alone, she makes  1%2F5  of the job per hour.


Working together, the two girls make  1%2F3 + 1%2F5 of the job per hour.


Let  t be the time (in hours) for the two girls to complete the job, working together.

Then they make  1%2Ft  part of the job per hour.


It gives you an equation


    1%2F3 + 1%2F5 = 1%2Ft.


At this point the setup is completed: the equation is constructed, and your next step is to solve it.


For it, multiply both sides by 15t = 3*5*t to rid off the denominators. You will get


    5t + 3t = 15.


Simplify and solve for t :


    8t = 15,

    t = 15/8 = 17%2F8 hours = 1 hour and 52.5 minutes.    ANSWER

Solved and completed.

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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.