Question

It takes Ms. Campbell 5 times as long as it takes Ms. Dorsey to paint a room. If Ms. Dorsey

helps Ms. Campbell, they can paint the room together in four hours. How long does it take each to paint the room individually?
****** PLEASE HELP******

Answer 1

Dorsey = 4.8 hours

Campbell = 24 hours

Explanation:

It takes "x" hours for Dorsey

So, it will take 5 times more for Campbell, so

It takes "5x" hours for Campbell

Rate is inverse of time, so rates are:

Dorsey: 1/x

Campbell: 1/5x

We know Rate * Time = Work

When together, it takes 4 hours to finish a work, so we can write:

`((1)/(x)+(1)/(5x))4=1`

Solving for x, we get the time of Dorsey:

`((1)/(x)+(1)/(5x))4=1\\((1)/(x)+(1)/(5x))=(1)/(4)\\(5+1)/(5x)=(1)/(4)\\(6)/(5x)=(1)/(4)\\5x=24\\x=4.8`

Dorsey takes 4.8 hours alone

Campbell takes 4.8 * 5 = 24 hours alone