SOLUTION: It takes Aaron 20 hours to paint a house. It takes Bob 30 hours to paint the same house. How long do both of them take if they work together to paint the same house?

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Question 1163216: It takes Aaron 20 hours to paint a house. It takes Bob 30 hours to paint the same house. How long do both of them take if they work together to paint the same house?
Found 3 solutions by jim_thompson5910, ikleyn, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Let's say there are 60 boards that need to be painted in total. This will effectively constitute painting the entire house. I picked 60 as it is the LCM of 20 and 30. This way when we divide later on, we get nice whole numbers.

When working alone, Aaron needs 20 hours to paint all 60 boards. His rate is 60/20 = 3 boards per hour.
When working alone, Bob takes 30 hours to paint 60 boards. His rate is 60/30 = 2 boards per hour.
If they work together, and neither slows the other down, then their combined rate is 3+2 = 5 boards per hour.

Let x be the number of hours needed if they both work together.
This multiplies with the combined rate we just got, so we have 5x representing the number of boards painted if they work together. Set this equal to 60 and solve for x

5x = 60
x = 60/5
x = 12

It will take them 12 hours to get the job done if they work together.

Answer: 12 hours

Answer by ikleyn(52909) About Me  (Show Source):
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.

Aaron makes  1%2F20  of the job per hour.


Bob makes  1%2F30  of the job per hour.


Working together, they make  1%2F20 + 1%2F30 = 3%2F60+%2B+2%2F60 = 5%2F60 = 1%2F12  of the job per hour.


It means that they will complete the job in 12 hours, working together.    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!
It takes Aaron 20 hours to paint a house. It takes Bob 30 hours to paint the same house. How long do both of them take if they work together to paint the same house?
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20*30/(20+30) = 600/50 = 12