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Puzzle:

  "Fischer and Myron just stepped side-by-side onto a moving escalator. They are climbing up the stairs, and counting steps as they climb. Myron is climbing more quickly than Fischer. Myron climbs three steps in the time it takes Fischer to climb only two steps. Neither of them skips any steps. Myron steps off at the top, having counted 25 steps. He waits at the top for the slower Fischer, who steps off having counted only 20 steps. How many steps are showing on the escalator at any instant?"




Solution:

*** For this question, I have developed my own solution and sent it to the author of "Heard on Wall Street". Hopefully it will appear in the latest version :D ***

- The keypoint is to find out the hidden relationship between space and time that most people may miss.

- We first denote different variables:
  d1: the distance traveled by the escalator at the moment Fischer just arrived at the top.
  d2: the distance traveled by the escalator at the moment Myron just arrived at the top.
  D: the distance shown on the escalator at any moment.
  vF: the velocity of Fisher.
  vM: the velocity of Myron.
- We know that when Myron has arrived at the top, the distance on the escalator is:

d1+25 = D
- When Fisher has reached the top:
d2+20 = D
- Thus, we know the distance the escalator has travelled while Myron has stopped but Fischer walks is:
d' = 5
  ***Why?: We just split the distances into people's distances and escalator's distance. Fisher only walks 25 steps, and Myron only walks 20 steps. D is constant at any time, so the difference 5 steps can only be the difference between the distances of the escalator.

- At the same time, we know:
vM : vF = 3:2
dM : dF = 3:2, when the time t is the same
dF = 23dM
- We know that Myron has travelled 25 km, so based on the ratio, the actual distance Fischer has walked after Myron has reached the final point is:
20 - 25 * 23 = 103
- The time that the escalator continues to move is the same as that of Fischer has walked after Myron, and their velocities are constant.

- The ratio of their total distances will be the same as the ratio of the distances they both move after Myron has stopped.
d' : 103 = d2 : 20
- We solve it, and get d2 = 30.

- If d2 = 30,
D = 30+20 = 50 steps.

*** Note: I have written a simple code to generalize this problem. If you want to check, please click on this link:
https://github.com/Kexin996/brainteaser/blob/master/july9.py