AMC 10 2008b Problem 6

Points $B$ and $C$ lie on $\overline{AD}$. The length of $\overline{AB}$ is $4$ times the length of $\overline{BD}$, and the length of $\overline{AC}$ is $9$ times the length of $\overline{CD}$. The length of $\overline{BC}$ is what fraction of the length of $\overline{AD}$? $\textbf{(A)}\ \frac{1}{36} \textbf{(B)}\ \frac{1}{13} \textbf{(C)}\ \frac{1}{10} \textbf{(D)}\ \frac{5}{36} \textbf{(E)}\ \frac{1}{5}$