Question

A homeowner estimates that it will take 9 days to roof his house. A professional roofer estimates that he could roof the house in 5 days. How long ( in days ) will it take if the homeowner helps the roofer?

Answer 1

If x denote the days, the rate unit being Jobs per day is:

`(1)/(x)=(1)/(9)+(1)/(5)`

this is equivalent to

`(1)/(x)=(5+9)/(45)=(14)/(45)`

solving for x, we get:

`x\text{ = }(45)/(14)=3.2\text{ days}`

that is just a little more than 3 days.