# A Simple Problem that seems to elude me

1. Feb 2, 2005

### TooManyHours

My mind is blank for some reason as I can't seem to figure out how to set up this problem...

It takes Steve and Dale together 10 hours to paint a house.

Steve takes 30 hours by himself.

How long would it take Dale to paint the house my himself?

Thanks...

2. Feb 2, 2005

### hypermorphism

Steve paints houses at a rate of (1 house)/(30 hours). Assuming Steve has a linear rate of painting, we have 3*(1/30) = 1/10, which means Steve paints 1/3 of a house in 10 hours. Can you continue ?

3. Feb 2, 2005

### TooManyHours

OK,

Steve paints 1 house in 30 hours or 1/3 house in 30/3 = 10 hours

That means that Dale has to paint the other 2/3 of the house in the 10 hour period.

Working backwards for Steve, to get from the 10 hours together to his single total, we multiply 10 by 3/1 = 30 hours.

So, for Dale, we have to multiply 10 * 3/2 to get 30/2 or 15 hours to paint the house by himself.

I think...

4. Feb 2, 2005