SOLUTION: Ana and Beth do a job together in three hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone? A.3 and 1/3 hours B.2 and 1/3 hours

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Question 1120003: Ana and Beth do a job together in three hours. Working alone, Ana does the job in 5 hours. How long will it take Beth to do the job alone?
A.3 and 1/3 hours
B.2 and 1/3 hours
C. 3 hours
D. 7 and 1/2 hours
Found 2 solutions by Shin123, ikleyn:
Answer by Shin123(626)   (Show Source): You can put this solution on YOUR website!
Ana can complete 1/5 of the job in a hour and Beth can complete x of the job in a hour. 1 divided by 1/5+x should be 3. So 1/5+x=1/3 .2+x=0.33333... x=0.133333333... x=2/15=1/7.5 Beth can complete 1/7.5 of the job in a hour. So the answer is D. Check out this solver,
- Solving Rate of Work Problems
Answer by ikleyn(52779)   (Show Source): You can put this solution on YOUR website!
.
It is a standard and typical joint work problem.

When you solve such a problem (as any other Math problem), it is important to get not only correct answer (number).

It is also important to get the solution, presented in clear, logical and correct form.

It is why I am writing my solution after the solution of the other tutor. 


    Ana does   of the job in hour.  In each hour.  It is her rate of job.


    Working together, Ana and Beth do   of the job per hour. It is their combined rate of work.


    Then it is clear that the Beth's individual rate of work is the difference   -  =  -  =  of the job per hour.


    It means that Beth can complete the job in  = 7.5 hours working alone.

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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.


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