SOLUTION: Jose can do a certain job in 10 days, and Roy can do the same job in 12 days. If two men work together, how many days would it takes to finish the job?

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Question 1186458: Jose can do a certain job in 10 days, and Roy can do the same job in 12 days. If two men work together, how many days would it takes to finish the job?
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.
Jose can do a certain job in 10 days, and Roy can do the same job in 12 days.
If two men work together, how many days would it takes to finish the job?
~~~~~~~~~~~~~~~ 

Jose makes  1%2F10 of the job per day.


Roy makes  1%2F12  of the job per day.


Working together, they make  1%2F10+%2B+1%2F12 = 6%2F60+%2B+5%2F60 = 11%2F60  od the day.


It means that wotking together they will complete the job in  60%2F11 = 5 5%2F11  days.    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.



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Jose can do a certain job in 10 days, and Roy can do the same job in 12 days. If two men work together, how many days would it takes to finish the job?
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10*12/(10+12) = 120/22
= 60/11 days.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


This kind of "working together" problem is so common that it is worthwhile to remember the simple formula shown by one of the tutors.

If you want to understand the standard formal algebraic method for solving the problem (which leads to that formula), use the method shown by the other tutor.

And for another method for solving this type of problem that many students prefer, you can try this:

Consider the least common multiple of the two given times of 10 days and 12 days, which is 60 days.
In 60 days, Jose could do 60/10=6 of these jobs and Roy could do 60/12=5 of them.
So together in 60 days the two of them could do 11 of the jobs.
And so the amount of time it would take the two of them together to do the one job is 60/11 days.