SOLUTION: Bob steps onto an escalator which is moving up to the 2nd floor. If he walks one step per second on it, he walks 20 steps to reach to the 2nd floor. If he walks 2 steps per seconds

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Question 1163590: Bob steps onto an escalator which is moving up to the 2nd floor. If he walks one step per second on it, he walks 20 steps to reach to the 2nd floor. If he walks 2 steps per seconds, he walks 30 steps to reach to the 2nd floor. Find the number of steps of the escalator when it is stationary.
Answer by ikleyn(52765) About Me  (Show Source):
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Bob steps onto an escalator which is moving up to the 2nd floor. If he walks one step per second on it,
he walks 20 steps to reach to the 2nd floor. If he walks 2 steps per seconds, he walks 30 steps to reach to the 2nd floor.
Find the number of steps of the escalator when it is stationary.
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Let x be the number of steps of the escalator when it is stationary (on one its side).


In the first scenario, Bob makes 20 steps on the escalator in 20 seconds --- hence, the escalator moves x - 20 steps in 20 seconds.


In the second scenario, Bob makes 30 steps on the escalator in 15 seconds --- hence, the escalator moves x - 30 steps in 15 seconds.


Escalator moves uniformly with the same speed/(rate) in both cases.


Hence, the ratio %28x-20%29%2F%28x-30%29  is the same as ratio of times  20%2F15 :


    %28x-20%29%2F%28x-30%29 = 20%2F15,  or

    %28x-20%29%2F%28x-30%29 = 4%2F3.


Cross-multiply and solve for x


    3*(x-20) = 4*(x-30)

    3x - 60 = 4x - 120

    120 - 60 = 4x - 3x

    60       = x.


ANSWER.  There are 60 steps of the escalator (on one its side).

Solved.