SOLUTION: A carpenter can do a job in four hours. His assistant can do the same job in six hours. How long would it take them to do the job together?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A carpenter can do a job in four hours. His assistant can do the same job in six hours. How long would it take them to do the job together?      Log On


   

Question 1093866: A carpenter can do a job in four hours. His assistant can do the same job in six hours. How long would it take them to do the job together?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613) About Me  (Show Source):
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
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The carpenter makes 1%2F4 of the job per hour. It is his rate of work.


The assistant makes 1%2F6 of the job per hour. It is his rate of work.


Working together, they make 1%2F4+%2B+1%2F6 = 6%2F24+%2B+4%2F24 = 10%2F24 = 5%2F12 of the job each hour.


      Notice that their rates are added !!  (Which is so natural . . . )



Hence, it will take 12%2F5 = 22%2F5 hours = 2 hours and 24 minutes for them to complete the job working together.


Lesson to learn from this solution 

    When solving rate of work problems,  think about rates of work, 
    and remember that the combined rate of two persons working together is the sum of the rates of individuals.


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It is a 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.