Question

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

Answer 1

Answer:

Dorsey = 4.8 hours

Campbell = 24 hours

Step-by-step 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:

$(\frac{1}{x}+\frac{1}{5x})4=1$

Solving for x, we get the time of Dorsey:

$(\frac{1}{x}+\frac{1}{5x})4=1\\(\frac{1}{x}+\frac{1}{5x})=\frac{1}{4}\\\frac{5+1}{5x}=\frac{1}{4}\\\frac{6}{5x}=\frac{1}{4}\\5x=24\\x=4.8$

Dorsey takes 4.8 hours alone

Campbell takes 4.8 * 5 = 24 hours alone