Answer:
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, [tex]\frac{1}{X}=\frac{1}{9}[/tex].
The work done by the professional roofer in 1 day is, [tex]\frac{1}{Y}=\frac{1}{3}[/tex]
The work done in 1 day if both the homeowner and the professional roofer work together is,
⇒ [tex]Work\ done\ in\ day=(\frac{1}{X}+\frac{1}{Y})=(\frac{1}{9}+\frac{1}{3})=\frac{1+3}{9}=\frac{4}{9}[/tex]
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,
⇒ [tex](X+Y)=\frac{1}{Work\ done\ in\ 1\ day}=\frac{1}{(\frac{4}{9}) } =\frac{9}{4} =2.25\ days[/tex]
Thus, the time it will take to roof the house if the homeowner helps the roofer is 2.25 days.
