Henry Ernest Dudeney/Modern Puzzles/34 - The Moving Stairway

by : $34$

 * The Moving Stairway
 * On one of the moving stairways on the London Tube Railway I find that if I walk down $26$ steps I require $30$ seconds to get to the bottom,
 * but if I take $34$ steps I require only $18$ seconds to reach the bottom.


 * What is the height of the stairway in steps?


 * The time is measured from the moment the top step begins to descend to the time I step off the last step at the bottom onto the level platform.

Solution

 * $46$ steps.

Proof
Let $S$ be the number of steps on the stairway.

Let $v$ be the speed of descent of the stairway in steps per second.

We are given that: