Keith can paint a house in 7 hours. If Fred helps, it takes them 6 hours. Without help, how long would it take Fred to do the same thing?

Question

Need an answer for my homework...just to see how to solve these kinds of problems. Step by step walk through would be really appreciated.

Answer 1

Micah, I hope I'm not too late to help!

 

In one hour, Keith can paint 1/7 of a house.  We see that together it takes 6 hours.  If we let f = Fred's time alone, in one hour, he'd do 1/f of a house.

 

1/7(6) + 1/f(6) = 1 (house)

 

6/7 + 6/f = 1

 

Our common denominator is 7f.  Because everything will be over the same denominator, we can get rid of it.

 

6f + 42 = 7f

         f = 42 hours

 

Man, Frank is slow!