Odell and Kershaw run for $30$ minutes on a circular track. Odell runs clockwise at $250 \, \text{m/min}$ and uses the inner lane with a radius of $50$ meters. Kershaw runs counterclockwise at $300 \, \text{m/min}$ and uses the outer lane with a radius of $60$ meters, starting on the same radial line as Odell. How many times after the start do they pass each other?

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