You can paint a room in 9 hours. If your friend helps​ you, it will take 4 hours to paint the room. How long would it take your friend to paint the room by​ himself?

Answer 1

In one hour you can paint the room in 1/9 of the time.

Your friend can paint it in 1/F of the time.

So 1/9 +1/F = 1/4

F=7.2 hours to paint it alone

Answer 2

Assume that the room is 3600 ft2 (this is arbitrary... you can use any reasonable number)

Then You paint 3600 ft2/9 hours = 400 ft2/ hour

Then Let the friends rate = x

So, x ft2/hour(4 hours) + 400 ft2/hour(4 hours) = 3600 ft2

Then x = 900 ft2/hour - 400 ft2/hour = 500 ft2/hour

So, 3600 ft2/(500 ft2/hour) = 7.2 hours for the friend to paint the room by himself!

Answer 3

Each of you has a speed measured in rooms per hour. Yours is 1/9

When you work together, the total job takes 4 hours. From that, you can find what portion you did: 1/9 rooms per hour * 4 hours = 4/9 of a room. Thus, your friend did 5/9 of a room. His rate is then (5/9)/4

(time = 1/rate)