What is the height of the stairway in steps?

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On one of the escalators on the London subway I find that if I walk down twenty-six steps I require thirty seconds to get to the bottom, but if I make thirty-four steps I require only eighteen 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.

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    If I walk 26 steps I require 30 seconds, and if I walk 34 steps I require only  18 seconds. Multiply 30 by 34 and 26 by 18 and we get 1,020 and 468,
    the difference between which is 552. Divide this by the difference between 30  and 18 (that is, by 12) and the answer is 46, the number of steps in the stair­ way, which descends at the rate of 1 step in 1 ~ seconds. The speed at which I walk on the stairs does not affect the question, as the step from which I alight will reach the bottom at a given moment, whatever I do in the mean­ time.

    ravi Expert Answered on 30th July 2015.
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