AHSME 1975 Problem 28

In $\triangle ABC$ shown in the adjoining figure, $M$ is the midpoint of side $BC, AB=12$ and $AC=16$. Points $E$ and $F$ are taken on $AC$ and $AB$, respectively, and lines $EF$ and $AM$ intersect at $G$. If $AE=2AF$ then $\frac{EG}{GF}$ equals

$\textbf{(A)}\ \frac{3}{2} \textbf{(B)}\ \frac{4}{3} \textbf{(C)}\ \frac{5}{4} \textbf{(D)}\ \frac{6}{5}\\ \textbf{(E)}\ \text{not enough information to solve the problem}$