SOLUTION: Allen can complete a job in 5 hours. If his son Anderson helps, it will take 3 hours to complete the work together. How long would it take to complete the work if Anderson works al

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Question 1157569: Allen can complete a job in 5 hours. If his son Anderson helps, it will take 3 hours to complete the work together. How long would it take to complete the work if Anderson works alone
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Working together, they make  1%2F3  of the job per hour.


Working alone, Allen makes  1%2F5  of the job per hour.


Hence, Anderson, working alone, makes  1%2F3+-+1%2F5 = 5%2F15+-+3%2F15 = 2%2F15 of the job per hour.


It means that Anderson will complete the job in 15%2F2 hours = 7.5 hours.    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 greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Here is an alternative to the standard algebraic solution method shown by the other tutor.

Allen can do the job alone in 5 hours. So when he and his son complete the job in 3 hours, Allen does 3/5 of the job.

That means his son does 2/5 of the job in 3 hours.

There are two easy paths to the answer from here.

(a) The amount of time it takes the son alone to do the job is 3/(2/5) = 3*(5/2) = 15/2 hours, or 7 1/2 hours.

(b) Since the son does 2/5 if the job in the time Allen does 3/5, the son works 2/3 as fast as Allen; therefore the amount of time it will take the son alone is 3/2 what it takes Allen alone: (3/2)*5 = 15/2 or 7 1/2 hours.