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Number of escalator steps

  1. Apr 14, 2015 #1
    1. The problem statement, all variables and given/known data
    There is a escalator and 2 persons move up it. A takes 50 steps and B takes 75 steps while the escalator is moving up. Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps, find the no. of steps in the escalator that is possible to see while it is staionary.?

    2. Relevant equations


    3. The attempt at a solution
    v is the speed of persons (A=1v, B=3v)
    x is the number of stairs
    y is the speed of escalator
    so:
    50/v=(x-50)/y
    75/3v=(x-75)/y
    I make from that:
    (50y/v)+50=x
    (25y/v)+75=x
    and then i remove fractions and have system of equations
    50y+50v=xv
    25y+75v=xv *(-2) equivalent adjustment

    50y+50v=xv
    -50y-150v=-2xv

    -100v=-xv
    -100=-x
    x=100
    Now I got the number of steps so if I do 100/2=50 is the number of steps we can see if it is stationary.

    I just want to ask if is everything right.
    And.. I´m not good in english so there are many mistakes in it, so sorry
     
  2. jcsd
  3. Apr 14, 2015 #2

    RUber

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    Homework Helper

    I don't see why you divided by 2 at the end.
    If only 50 steps are visible, how would B have taken 75 to get to the top?
     
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