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 3L3L, and Bob's wall has length 2L2L.

They both push off of their walls at the same instant. Alfred has a speed of 3v3v, and Bob has a speed of 5v5v. They both stop when they reach their opposing walls.

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

Find a+ba+b.

Ignore gravity and air resistance.


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