Denote by t the time we ned to paint a fence, by l the length of the fence and by n the number of painters. Then, we have the next equation
[tex]t=k\frac{l}{n}[/tex]It takes 5 hours and 30 minutes, that is
[tex]5(60)+30=330\text{ minutes}[/tex]to paint a l=150 feet fence with n=3 painters, then
[tex]\begin{gathered} 330=k\frac{150}{3} \\ k=\frac{3\times330}{150} \\ k=\frac{33}{5} \end{gathered}[/tex]
So, if we have a l=510 feet fence and n=7 painters, then we will need
[tex]\begin{gathered} t=\frac{33}{5}\cdot\frac{510}{7} \\ t=480.85\text{ minutes} \end{gathered}[/tex]That is, approximately 8 hours.
