Question

You can paint a room in 8 hours. Working together, you and a friend could paint the same room in just 5 hours. How long would it take your friend to paint the room alone.

Answer 1

friend alone could do it in 13 hours and 1/3

Explanation:

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 1/3