# Answer to Question #2788 in Abstract Algebra for d4522

Question #2788

Matt can clean his house in 6 hours and his sister can do it in 9 how long will it take the two together?

Expert's answer

Let's denote the work to be done as X, thus productivity of Matt is X/6 , of sister X/9. If they work together, theirs productivity should be added.& Therefore, the time is&

(work to be done)/(productivity) = X/(X/6 + X/9) = 1/(1/6 + 1/9) = 1/ (5/18) = 18/5 = 3,6 hours.

(work to be done)/(productivity) = X/(X/6 + X/9) = 1/(1/6 + 1/9) = 1/ (5/18) = 18/5 = 3,6 hours.

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