Question 4
Let $R = (8, 6).$ The lines whose equations are $8y = 15x$ and $10y = 3x$ contain points $P$ and $Q,$ respectively, such that $R$ is the midpoint of $\overline{PQ}.$ The length $PQ$ equals $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$