Question 883050
Well you had the right idea but your set up is a little flawed.  

If we let R = the time it takes Ronnie to paint a room and T = the time it takes Tim to pain a room then we have the following equations:

R = 4+T
R+T = 9 

Now we see that R is already by its self in the first equation so lets just plug that in for R in the second equation and solve for T.

R+T = 9
4+T+T = 9
4+2T = 9
2T = 5
T = 5/2

So we know that it takes Tim 5/2 hours to paint the room which is 2 and a half hours.  Now we can plug that 5/2 into the first equation and find how long it takes Ronnie.  

R = 4+T
R = 4 + 5/2
R = 8/2 + 5/2
R = 13/2

So it takes Tim 5/2 hours or 2 and a half hours to paint the room while it takes Ronnie 13/2 hours or 6 and a half hours to paint the same room.