SOLUTION: Dan can do the job in 30 hours, Ellen can do it in 40 hours, and Francis can do it in 60 hours. How long would it take them if they work together? (use only one variable)(thanks in

Question 1132152: Dan can do the job in 30 hours, Ellen can do it in 40 hours, and Francis can do it in 60 hours. How long would it take them if they work together? (use only one variable)(thanks in advance)
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Dan can do the job in 30 hours, Ellen can do it in 40 hours, and Francis can do it in 60 hours. How long would it take them if they work together?
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h hours.
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1/h = 1/30 + 1/40 + 1/60

Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.

Dan makes of the entire job per hour. It is his rate of work. Ellen makes of the entire job per hour. It is her rate of work. Francis makes of the entire job per hour. It is his (or her (?) ) rate of work. Working together, the tree persons make = = = of the entire job per hour. It is their COMBINED rate of work, which is the sum of the individual rates. To solve the problem using one variable, introduce t as the time it takes them to complete the entire job working together. Then your equation is Time*Rate = the entire job, or = 1, which implies t = = = hours = 13 hours and 20 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.

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