In the figure, $\overline{LQ}$ intersects $\overline{MP}$ at point $R$, and $\overline{LM}$ is parallel to $\overline{PQ}$. The lengths of $\overline{MR}$ and $\overline{RP}$ are 9 and 15, respectively. If the total length of $\overline{LQ}$ is 24, what is the length of $\overline{LR}$?