you can paint a room in 8 hours. your friend and you can paint a room in 5 hours together. how long does it take your friend alone?

Answer 1

Your rate = room/8
friends rate = room/x
combined rate = room/8 + room/x
= room(x+8)/(8x)

then
5 = room / [room(x+8)/(8x)]
5 = 8x/(x+8)
8x = 5x + 40
3x = 40
x = 40/3 = 13 1/3

friend alone could do it in 13 hours and 20 minutes