A circular track with diameter $500$ is externally tangent at a point A to a second circular track with diameter $1700.$  Two runners start at point A at the same time and run at the same speed.  The first runner runs clockwise along the smaller track while the second runner runs clockwise along the larger track.  There is a first time after they begin running when their two positions are collinear with the point A.  At that time each runner will have run a distance of $\frac{m\pi}{n}$ where  $m$  and  $n$ are relatively prime positive integers.  Find  $m + n. $

Let's think step by step and output the final answer within \boxed{}.
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