Conversation

I think you can do better than this path if you and the other person coordinate on timing. Even though the other person doesn't stray from the center line, she may slow down to help you minimize the distance you travel.
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Yep! Another way of stating that is to assume you’re The Flash. Then you can zoom to (6,6), wait for the other person to pass (12-6sqrt2,0), and then zoom to (12,0), for a minimal distance of 12sqrt2 = 16.97