Height of stairways


stairway height puzzle
Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick cal-culations in my mind. I found that if I walk down twenty-six steps, I require thirty seconds to reach the bottom. However, if I am able to step down thirty-four stairs I would only require eighteen seconds to get to the bottom.
If 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, can you tell the height of the stairway in steps?

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  • 1 Answer(s)

    If I walk 26 steps I require 30 seconds.
    If I walk 34 steps I require only 18 seconds. Multiplying the 30 by 34 and 26 by 18 we get 1020 and 468.
    The difference between 1020 and 468 is 552. When we divide this number by the difference between 30 and 18-, i.e. by 12 we get the answer 46—the number of steps in the stairway.

    John123 Expert Answered on 26th July 2015.
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