Walk the straight and narrow: The Wknd Puzzle by Dilip D’Souza

Since I had time to kill and since I have a mostly idle mind, I found myself counting and musing as I made my way along that corridor. Here are some of those numbers.

I took the first moving walkway: 32 steps from one end to the other. The second, I walked alongside: 40 steps from one end to the other. Assume all the walkways are the same length and have the same speed of motion; also that I walk at the same speed whether I’m on a walkway or not, ie, I take my steps at the same pace.

Question 1: In percentage terms, what is the speed of the walkways compared to my walking speed?

Just for fun, I turned around and tried walking back along the second walkway, ie, against its motion.

Question 2: How many steps did I need to get from one end to the other?

Hint: To make this easier, assume the walkways are 100 metres long, and it takes me 100 seconds to walk the stretch off the walkway.

Scroll down for the answers.

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Answer 1: On the walkway, it takes 32 steps instead of 40 to cover the same distance. So it takes 32/40 = 80% of the time it takes me off the walkway, or just 80 seconds. So my speed is 100 metres/80 seconds (on) compared to 100 metres/100 seconds (off), or 1.25 m/s vs 1 m/s. Thus the walkway adds 0.25 m/s to my speed, or it is moving at 25% of my walking speed.

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

Bonus for you to figure out: Do you need the hint?

PS: 100 metres in 40 steps is ridiculous.