SOLUTION: A man can paint a room by himself in 8 hours and it takes his son 12 hours to do the same job. The man works by himself for three hours, then his son joins him and the two together

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A man can paint a room by himself in 8 hours and it takes his son 12 hours to do the same job. The man works by himself for three hours, then his son joins him and the two together      Log On


   

Question 204667: A man can paint a room by himself in 8 hours and it takes his son 12 hours to do the same job. The man works by himself for three hours, then his son joins him and the two together complete the job. How long does the son work?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If the man can paint the room in 8 hours, then he can paint 1%2F8 of the room in 1 hour.
If his son can paint the room in 12 hours, then he can paint 1%2F12 of the room in 1 hour.
Now if the man works by himself for 3 hours, then he can paint:
3%2A%281%2F8%29+=+3%2F8 of the room which leaves 5%2F8 of the room to paint.
Now the man and his son, working together can paint 1%2F8+%2B+1%2F12+=+5%2F24 of the room in 1 hour.
So the question is, how long would it take the father & son together to finish the 5%2F8 of the room?
To find this, we'll divide the 5%2F8 by 5%2F24.
%285%2F8%29%2F%285%2F24%29+=+%285%2F8%29%2A%2824%2F5%29 = 3.
The son works for 3 hours.