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

Modern Puzzles by Henry Ernest Dudeney: $34$

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.

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Arithmetical and Algebraical Problems: Locomotion and Speed Puzzles: $34$. -- The Moving Stairway
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Speed & Distance Puzzles: $62$. The Escalator