Question

A homeowner estimates that it will take 11 days to roof his house. A professional roofer estimates that he could roof the house in 6 days. How long will it take if the homeowner helps the roofer?

Answer 1

Answer:

It will take 3.88 days

Step-by-step explanation:

Let x= Number of days it will take both the homeowner and the roofer to roof the house.

After x days, we can know that:

1. The homeowner will do:

$\frac{x}{11}$ of the job

2. The roofer will do:

$\frac{x}{6}$ of the job

Furthermore:

$\frac{x}{11}+\frac{x}{6}=1$ Because both complete the whole job

Solving this equation:

$\frac{x}{11}+\frac{x}{6}=1 \\ \\ Multiplying \ by \ 66: \\ \\ 66(\frac{x}{11}+\frac{x}{6}=1) \\ \\ 66(\frac{x}{11})+66(\frac{x}{6})=66 \\ \\ 6x+11x=66 \\ \\ 17x=66 \\ \\ Dividing \ by \ 17: \\ \\ x= \frac{66}{17}=3.88 \ days$