Escalator Problems

@stevenstrogatz reposts a clever, simple problem:

two people climb a staircase and then climb an escalator. One person rests a minute on the staircase and the other rests a minute on the escalator, but otherwise they climb stairs at the same rate. Who is faster or are they equally fast?

There’s also an airport-walkway version that adds special relativity as a twist.

It’s interesting to see the varied thought processes in the comments. Pencil and paper is often quicker and yields useful analytic insight, but these are both accumulation problems, and therefore good candidates for SD simulation.

How would you model this situation? (I’ll post my answer in a day or two.)

2 thoughts on “Escalator Problems”

  1. My initial gut feeling told me they will arrive at the same time. I thought it is so since the rest time is additive and does not affect the speed directly. However, then I started doubting myself and writing equations. First simple equations to represent time as a function of speed/distance. However, in this case the speed is a function of distance travelled and the distance travelled is a function of speed, it needs to be expressed as differential equations. The additional problem that I experienced is that the differential equation has conditions, so the integrated function does not stay the same and then I would need to consult my old math textbooks to do the integration. Instead, I built an SD model in Stella and ran 10 different scenarios. All of which shows that it does not matter where the person takes their break, the total time travelled remains the same. I think this is the case since the integration of 0 is a constant, independent of time/distance or speed.

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