Question

Jonathan can paint a room in 8 hrs. After painting for 2 hours, his brother, David joined him and together, they finished painting the room in 3 1/3hours. In how many hours will David finish painting the room alone?

Answer 1

Jon's rate ---- room/8
David's rate --- room/x
combined rate = room/8 + room/x
= (xroom + 8room)/(8x)
= room(x+8)/(8x)

but only (3/4)room remains to be painted.
so ..
(3/4)room/( (room(x+8)/(8x) ) = 10/3
(3/4) (8x)/(x+8) = 10/3
72x = 40x + 320
32x = 320
x = 10

Working alone he could have done the whole room in 10 hours, so it would take him 7.5 hours to finish the room