Question 1027602
.
Working alone, a painter can paint a living room in 6 hours.  A second painter can do the job in 9  hours.  How long will it take them to paint the room if they work together?  State what x represents, state the equation, and then state the answer.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
Since the first painter can paint a living room in 6 hours, he paints {{{1/6}}} of the living room area in one hour. It is his rate.

The other painter paints {{{1/9}}} of the living room area in one hour.

When the two painters work together, they paint {{{1/6 + 1/9}}} = {{{3/18 + 2/18}}} = {{{5/18}}} of the room area per hour.

Hence, they need {{{18/5}}} = {{{3}}}{{{3/5}}} hour = 3 hours and 36 minutes to complete the job, if they work together.


It is typical problem on joint work.

For a variety of similar solved jpint-work problems see the lesson <A HREF=https://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, 
and also associated lessons.
</pre>