Should I Rest at the Travelator or Not at the Travelator?
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This is a real-life puzzle encountered by one of my friends, again. After landing and arriving at the airport, I want to pick my baggage up quickly. The problem is that the baggage claim is $500$ m away. Luckily, along the way there are many travelators. Let's say, the total length of travelators is $250$ m (hence, the total length of non-travelators is also $250$ m). The travelator speed is $1$ m/s. I can also walk in $1$ m/s but I need to reserve $10%$ of my walking time to take a rest. How long and where should I take the rest to quickly arrive at the baggage claim? Should I rest at the travelator or not at the travelator? Note : Assume you are going to walk for $700$ s, you need to take a rest for $70$ s and can only truly walk for $630$ s. Let's say there is no travela...