Social Studies: 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?

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A homeowner estimates that it will take him 9

mike2910

18.01.2022

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, $\frac{1}{X}=\frac{1}{9}$ .

The work done by the professional roofer in 1 day is, $\frac{1}{Y}=\frac{1}{3}$

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

⇒ $Work\ done\ in\ day=(\frac{1}{X}+\frac{1}{Y})=(\frac{1}{9}+\frac{1}{3})=\frac{1+3}{9}=\frac{4}{9}$

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,

⇒ $(X+Y)=\frac{1}{Work\ done\ in\ 1\ day}=\frac{1}{(\frac{4}{9}) } =\frac{9}{4} =2.25\ days$

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

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