Answer to Question #2788 in Abstract Algebra for d4522

Question

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

Answer 1

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.