Question 1163496: An escalator is moving downward from 2nd floor to the 1st floor. Emily walks down from the 2nd floor to the first floor, and she walks 40 steps. Albert walks up from the first floor to the second floor, and he walks 80 steps. If Albert walks twice as fast as Emily, find the number of steps of the escalator when it is stationary.
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
An escalator is moving downward from 2nd floor to the 1st floor. Emily walks down from the 2nd floor to the first floor,
and she walks 40 steps. Albert walks up from the first floor to the second floor, and he walks 80 steps.
If Albert walks twice as fast as Emily, 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 (the number under the problem's question).
During the time Emily makes her walk down, the escalaror moves (x-40) steps.
During the time Albert makes his walk up, escalaror moves (x-80) steps.
Albert moves twice as fast as Emily, which means that Emily's time is twice the Albert's time.
But the escalator speed is a constant, so
x - 40 = 2*(x-80).
It is your basic equation from the condition to find x.
From the equation
x - 40 = 2x - 160
160 - 40 = 2x - x
x = 120.
ANSWER. The number of steps of the escalator when it is stationary is 120 (in one direction).
Solved.
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