Question 1021553
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sally can paint a room in 7 hours while it takes steve 9 hours how long would it take them to paint a room together?
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Sally's rate of painting room is {{{1/7}}} of the painting area per hour.

Steve's rate of painting room is {{{1/9}}} of the painting area per hour.

Their combined rate is {{{1/7 + 1/9}}} = {{{9/63 + 7/63}}} = {{{16/63}}} of the painting area per hour.

Hence, it will take {{{63/16}}} = {{{3}}}{{{15/16}}} of an hour for Sally and Steve to paint the room, if they work together.
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For many other similar solved problems on joint work see the lesson 
<A HREF=http://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using fractions to solve word problems on joint work</A> in this site.