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:
[tex](\frac{1}{x}+\frac{1}{5x})4=1[/tex]
Solving for x, we get the time of Dorsey:
[tex](\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[/tex]
Dorsey takes 4.8 hours alone
Campbell takes 4.8 * 5 = 24 hours alone
