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 $\overline{LR}$ are 10 and 12, respectively. If the length of $\overline{MP}$ is 25, what is the length of $\overline{LQ}$?