Question 158
Consider a $1 \times 1$ grid of squares. Let $A, B, C, D$ be the vertices of this square, and let $E$ be the midpoint of segment $CD$. Furthermore, let $F$ be the point on segment $BC$ satisfying $BF = 2\,CF$, and let $P$ be the intersection of lines $AF$ and $BE$. Find $\frac{AP}{PF}$.