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:It will take 3.88 daysStep-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 job2. The roofer will do: [tex]\frac{x}{6}[/tex] of the jobFurthermore:[tex]\frac{x}{11}+\frac{x}{6}=1[/tex] Because both complete the whole jobSolving 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]