# A) An escalator is 10 m long. If a person stands on the “up” escalator, it takes 65 s to ride to the top. If a person walks up the moving escalator with a speed of 0.35 m/s relative to the...

A) An escalator is 10 m long. If a person stands on the “up” escalator, it takes 65 s to ride to the top. If a person walks up the moving escalator with a speed of 0.35 m/s relative to the escalator, how long does it take to get to the top? Answer in units of s. B) If a person walks down the “up” escalator with the same relative speed as in Part 1, how long does it take to reach the bottom? Answer in units of s.

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### 1 Answer

First we will calculate the speed of movement of the escalator. Since the length is 10 m, and the travel time is 65 s, the speed of a step is:

v = d/t = 10/65 = 0.15 m/s

If the person walks up or down with the ladder in motion, we must apply the principle of composition of speeds. In this case it is simple because the speeds have the same direction in both cases.

If the person, walks towards the top, adds his speed to the speed of the escalator and time is:

vp + ve = d/t

t = d/(vp + ve)

t = 10/(0.35 + 0.15) = 20 s

If the person walks towards the bottom, in the "up" escalator, its speed is subtracted from the speed of the escalator and time is:

vp - ve = d/t

t = t = d/(vp - ve)

t = 10/(0.35 - 0.15) = 50 s