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Math Help - "Down the Escalator"

  1. #1
    Newbie zenith20's Avatar
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    Question [solved]"Down the Escalator"

    27) Down the Escalator
    Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind, 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?

    ---------------------
    who can solve this? (explain the solution plz)

    Last edited by zenith20; September 1st 2010 at 07:55 PM.
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  2. #2
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    Quote Originally Posted by zenith20 View Post
    27) Down the Escalator
    Recently, while in London, I decided to walk down the escalator of a tube station. I did some quick calculation in my mind, 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?

    ---------------------
    who can solve this? (explain the solution plz)

    let r = rate the escalator moves in steps per second

    h = height of the escalator in steps

    h = \left(r + \frac{26}{30}\right) \cdot 30

    h = \left(r + \frac{34}{18}\right) \cdot 18<br />

    setting each expression for h equal ...

    \left(r + \frac{26}{30}\right) \cdot 30 = \left(r + \frac{34}{18}\right) \cdot 18<br />

    30r + 26 = 18r + 34

    12r = 8

    r = \frac{2}{3} steps/sec

    substitute this value for r into either expression for h ...

    h = \left(\frac{2}{3} + \frac{26}{30}\right) \cdot 30

    h = 20 + 26 = 46 steps
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  3. #3
    Newbie zenith20's Avatar
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    Dear Skeeter, thanks for your solution really appreciated.
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