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It takes 12 hours for Adam to paint a certain wall ; 8 hours for Ben to paint the same wall.

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It takes 12 hours for Adam to paint a certain wall ; 8 hours for Ben to paint the same wall.

by Max@Math Revolution » Tue Sep 15, 2020 1:17 am

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(Work rate) It takes 12 hours for Adam to paint a certain wall, and 8 hours for Ben to paint the same wall. Adam painted alone for 3 hours, and then Ben came to help Adam paint. After a while, Adam left, and Ben finished the job on his own in 1 hour. How many hours did Adam and Ben work together?

A. 1
B. 3
C. 5
D. 7
E. 9
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Re: It takes 12 hours for Adam to paint a certain wall ; 8 hours for Ben to paint the same wall.

by Max@Math Revolution » Thu Sep 17, 2020 3:37 am
(Solution):

Adam takes 12 hours to paint a certain wall. In 1 hour, Adam will paint\(\frac{1}{12}\) of the wall.

Ben takes 8 hours to paint a certain wall. In 1 hour, Adam will paint \(\frac{1}{8}\) of the wall.

Adam started work and painted alone for 3 hours. Therefore, the amount of work done by Adam is:

=> \(\frac{1}{12}\) * 3 = \(\frac{1}{4}\) .


Adam and Ben together can finish (\(\frac{1}{12}\) + \(\frac{1}{8}\) = \(\frac{5}{24}\) ) work in 1 hour.

Ben painted for 1 hour alone at the end. Therefore, the amount of work done by Ben is:

=> 1 * \(\frac{1}{8}\) = \(\frac{1}{8}\).

Total work done:

=> \(\frac{1}{4}\) + \(\frac{1}{8}\) = \(\frac{3}{8}\).

Remaining work:

=> 1 - \(\frac{3}{8}\) = \(\frac{5}{8}\) of the work.

This work was done by Adam and Ben together:

=> \(\frac{5}{24}\) work in 1 hour = \(\frac{5}{8}\) the part of work to be completed in 3 hours since ( \(\frac{5}{24}\)) * 3 = \(\frac{5}{8}\).

Hence, Adam and Ben worked together for 3 hours.

Therefore, B is the correct answer

Answer B
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