Matt can paint a room in 5 hours and elliot can paint a room in 3 hours. how long will it take them to paint the room together?

Let x= the time each one paints at the same time. Painting one whole room means that the output of our equation equals1.

x/5 = the fraction of the room Matt can paint in x hours.
x/3 = the fraction of the room Elliot can paint in x hours.

Our working equation will be: x/5+x/3 = 1 
[solve for x]
[start by finding common denominator] 3x/15 + 5x/15=1
[add together] 8x/15 = 1
[isolate the variable] 8x=15
x=15/8, or 1 7/8 hours. Together, they can paint a room together in 1 7/8 hours. (An hour, 52 minutes, 30 seconds if you divide it all the way out!)