2001 AIME II Problem 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 of PQ equals \frac {m}{n}, where m and n are relatively prime positive integers. Find m + n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.