You walk upwards on an escalator, with a speed of 1 step per second. After 50 steps you are at the end. You turn around and run downwards with a speed of 5 steps per second. After 125 steps you are back at the beginning of the escalator.

The Question:
How many steps do you need if the escalator stands still?

For something somewhat related please see "Walking down an escalator".

Let h = elevator height (in steps)
     s = elevator upward speed (in steps per second)

Then upward speed     = 1 + s = h/50
        downward speed = 5 -  s = h/25

Adding the two equations,
   6 = 3h/50

h = 100 steps (our puzzle answer)
s = 1 step per second, upward

Our effective speed is 2 steps per second up, and 4 steps per second down

Posted by Steve Herman on 2008-09-12 12:21:41