Tying your shoelace on the moving walkway

Question

You are walking to your gate at a constant pace. Part of the corridor has a moving walkway that carries you forward at a fixed speed in addition to your own walking speed. 1. You must stop for a few seconds to tie your shoelace. Do you lose less time if you stop while on the walkway or while off it? 2. You have enough energy to run (instead of walk) for a fixed number of seconds. Do you gain more time by running on the walkway or off it?

Accepted Answer

Tie your shoelace on the walkway. Run where there is no walkway. The shoelace. While you stand still tying it, you cover zero distance if you are off the walkway, but you keep moving at the walkway's speed if you are on it. The stop costs a fixed number of seconds either way; doing it on the walkway means those seconds still make progress. So stop on the walkway. The running. Running for a fixed time t at an extra speed r buys you an extra distance r × t wherever you do it. The question is how much time that extra distance saves. Off the walkway, you would otherwise cover that distance at you…

Tying your shoelace on the moving walkway

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