# Crossing Paths in a Space Station

Two astronauts, Alfred and Bob, are positioned at the midpoints of adjacent walls, in a rectangular room, in a space station. Alfred's wall has length $$3L$$, and Bob's wall has length $$2L$$.

They both push off of their walls at the same instant. Alfred has a speed of $$3v$$, and Bob has a speed of $$5v$$. They both stop when they reach their opposing walls.

The closest distance they ever get to each other can be written as $$\frac{L}{a\sqrt{b}}$$, where $$a$$ and $$b$$ are positive integers and $$b$$ is square free.

Find $$a+b$$.

Ignore gravity and air resistance.

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