A girl wants to count the steps of a moving escalator which is going up if she is going up she counts 60 steps if she is going down taking the same time per step then she counts 90 steps how many steps would she have to take in either direction if the escalator were standing still?

Question

Mathematics

Lillian Wong

28 January, 20:14

A girl wants to count the steps of a moving escalator which is going up if she is going up she counts 60 steps if she is going down taking the same time per step then she counts 90 steps how many steps would she have to take in either direction if the escalator were standing still?

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Answers (1)

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Ming · Answer 1

Hello,

Let's assume t the time for counting one step

V the girl velocity in t

v the escalator velocity in t

d the length to go upstairs

going up: V*60+v*60=d

walking down: V*90-v*90=d

so

V+v=d/60

V-v=d/90

2V=d*5/180

V=d*5/360

V=d/72

V*72=d The girl must count to 72 steps. (here v=0)