Dan the dog spots Cate the cat 50 meters away. At that instant, Cate begins running away from Dan at 6 m/s, and Dan begins running toward Cate at 8 m/s. Both of them accelerate instantaneously and run in straight lines. Compute the number of seconds it takes for Dan to reach Cate.

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