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:
[tex]\frac{x}{11}[/tex] of the job
2. The roofer will do:
[tex]\frac{x}{6}[/tex] of the job
Furthermore:
[tex]\frac{x}{11}+\frac{x}{6}=1[/tex] Because both complete the whole job
Solving this equation:
[tex]\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[/tex]
