A homeowner estimates that it will take him 9 days to roof his house. A professional roofer estimates that he could roof the house in 3 days. How long will it take if the homeowner helps the roofer?

The time it will take to roof the house if the homeowner helps the roofer is 2.25 days.

Explanation:

The time it takes the homeowner to roof his house is, X = 9 days.

The time it takes the professional roofer to roof the house is, Y = 3 days.

Then if the the homeowner helps the roofer, the time it will take to roof the house is, X + Y.

The work done by the homeowner in 1 day is, .

The work done by the professional roofer in 1 day is,

The work done in 1 day if both the homeowner and the professional roofer work together is,

⇒

Then the number of days it takes to roof the house if both the homeowner and the professional roofer work together, i.e. X + Y is,

⇒

Thus, the time it will take to roof the house if the homeowner helps the roofer is 2.25 days.

answer; the trial de novo