SOLUTION: A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days later the coworker joins in to help finish the job,

Question 1108519: A painter can paint a building in 15 days and a coworker can do the same job in 10 days. If the first painter starts and 3 days later the coworker joins in to help finish the job, how many days does it take to paint the building?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Co-worker works for x days.

If the question were, "how many days does the co-worker help in finishing the painting job", then solve the equation for x.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
What fraction of the job does 1st painter
get done in 3 days?
His rate of painting is [ 1 building ] / [ 15 days ]

That means there is of the building
left to paint
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Add their rates of painting to get their rate
painting together
Let = their time in days to paint
of the building working together

Multiply both sides by

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Add the 3days to 4.8 days

It takes 7.8 days to paint the building
-----------------------------------
check the math & get a 2nd opinion if needed

Answer by ikleyn(52793)   (Show Source): You can put this solution on YOUR website!
.

The first painter makes of the job per day; it is his rate of work. In three days he did = of the job; hence, of the job remained. The second painter makes of the job per day; it is his rate of work. Hence, their combined rate of work is + = + = = of the job per day. Hence, it will take = = = of the day for the two painters to complete the painting.

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So, my answer coincides with that by @jomiceli.

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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.

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