On a current journey to Chennai, I took the Metro to and from the airport. At the airport, a protracted hall connects the Metro station to the arrival/departure space. To allow you to with the stroll, there’s a collection of transferring walkways. (What are they known as, “travelators”?)

Since I had time to kill and since I’ve a principally idle thoughts, I discovered myself counting and musing as I made my manner alongside that hall. Here are a few of these numbers.

I took the first transferring walkway: 32 steps from one finish to the different. The second, I walked alongside: 40 steps from one finish to the different. Assume all the walkways are the identical size and have the identical velocity of movement; additionally that I stroll at the identical velocity whether or not I’m on a walkway or not, ie, I take my steps at the identical tempo.

Question 1: In share phrases, what’s the velocity of the walkways in comparison with my strolling velocity?

Just for enjoyable, I rotated and tried strolling again alongside the second walkway, ie, in opposition to its movement.

Question 2: How many steps did I must get from one finish to the different?

Hint: To make this simpler, assume the walkways are 100 metres lengthy, and it takes me 100 seconds to stroll the stretch off the walkway.

Scroll down for the solutions.

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Answer 1: On the walkway, it takes 32 steps as an alternative of 40 to cowl the identical distance. So it takes 32/40 = 80% of the time it takes me off the walkway, or simply 80 seconds. So my velocity is 100 metres/80 seconds (on) in comparison with 100 metres/100 seconds (off), or 1.25 m/s vs 1 m/s. Thus the walkway provides 0.25 m/s to my velocity, or it’s transferring at 25% of my strolling velocity.

Answer 2: This time, the walkway reduces my velocity by 0.25 m/s; ie, to 0.75 m/s. The identical 100-metre distance takes 100/0.75 = 133.3 seconds. Since I stroll 40 steps in 100 seconds (off), I want 40/0.75, or simply over 53 steps (on); ie, I’ll get off the walkway on my 54th step.

Bonus so that you can determine: Do you want the trace?

PS: 100 metres in 40 steps is ridiculous.

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