AMC 12 2008b Problem 8

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 $\overline{AD}$?

(Solution)

\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}