SOLUTION: Person A can paint the neighbors house 2 times as fast as person B. The year A and B worked together, it took them 2 days. how long would it take each to paint the house?

Question 1137025: Person A can paint the neighbors house 2 times as fast as person B. The year A and B worked together, it took them 2 days. how long would it take each to paint the house?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

Painter A works as effectively, as two painters B. So, you can reformulate the problem in this way, saying that THREE painters B complete the painting job in 2 days. It means that one painter B, working alone, will make the entire job in 2*3 = 6 days. Hence, painter A, who works 2 times as fast as B, will complete the job in 3 days. ANSWER. Painter A - 3 days; painter B - 6 days.

Solved   //   mentally (without using equations).

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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)   (Show Source): You can put this solution on YOUR website!

The response from tutor @ikleyn shows one good way of solving the problem using logical reasoning and some simple arithmetic.

Here is another similar way to solve the problem.

Since A works twice as fast as B, when they work together A does 2/3 of the job.

Then, since together the two of them take 2 days to paint the house, the time required by A alone would be 2*(3/2) = 3 days.

And so then the time required by B alone would be twice that, or 6 days.
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