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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?"
*** 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:
- At the same time, we know:
- The ratio of their total distances will be the same as the ratio of the distances they both move after Myron has stopped.
- If d2 = 30,
*** 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