We have a closed loop walking track of 1 km in our neighbourhood. Some walkers go clockwise, some anticlockwise. If I'm one of the walkers who is going clockwise, and I keep meeting another walker who is walking anticlockwise at different spots in the closed loop track, as I and the other walker circle the track, how do I know which walker is going fast/slow? Of course, if both of us meet at the same spot, I know that both of us are doing the same speed.
Assumptions: 1. Both walkers maintain constant speed. 2. I have a phone that can give me my lap time. I can also find the time between successive meetings on the track with the help of the same phone. (Hint?) No other aid is available.
No formal proof is required. Only intuitive answer with justification will do.
Post Script: All of the above is actual. Not a hypothetical question. We need to remember that both walkers may not begin at the same time from the starting point. Indeed that would be the norm, rather than the exception. For example, I may meet the other walker just after I start my clockwise traverse.
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