AMC 8 2019 Problem 24

In triangle $\triangle ABC$, point $D$ divides side $\overline{AC}$ so that $AD:DC=1:2$. Let $E$ be the midpoint of $\overline{BD}$ and let $F$ be the point of intersection of line $\overline{BC}$ and line $\overline{AE}$. Given that the area of $\triangle ABC$ is $360$, what is the area of $\triangle EBF$?

$\textbf{(A) }24 \textbf{(B) }30 \textbf{(C) }32 \textbf{(D) }36 \textbf{(E) }40$