Answer:
4.5 days.
Step-by-step explanation:
Let n represent number of days it will take Trevor to paint 3/4 of the fence.
We have been given that Trevor paints 1/6 of the fence surrounding his farm each day. So part of fence painted in n days would be [tex]\frac{1}{6}n[/tex].
As Trevor needs to paint 3/4 of the fence, so we can set an equation as:
[tex]\frac{1}{6}n=\frac{3}{4}[/tex]
[tex]\frac{6}{1}\times \frac{1}{6}n=\frac{6}{1}\times\frac{3}{4}[/tex]
[tex]n=\frac{6\times3}{4}[/tex]
[tex]n=\frac{18}{4}[/tex]
[tex]n=\frac{9}{2}[/tex]
[tex]n=4.5[/tex]
Therefore, it will take Trevor 4.5 days to paint 3/4 of the fence.
