Question

A girl wants to count the steps of a moving escalator which is going up. If she counts 60 steps going up and 90 coming down. How many steps would she have to take in either direction if the escalator were standing still?

Answer 1

Let

V the speed of the girl per step
v the speed of the escalator per step
L the length between ground and floor in number of steps

V*60+v*60=L => V+v=L/60
V*90-v*90=L => V-v=L/90

By adding the equations V+v=L/60 and V-v=L/90 we get:

2V=L(3+2)/180

V=5L/360

V = L/72

Time to climb (in steps) with v=0 (escalator standing still) is:

V*t=L

t = L/V

t = L/(L/72)

t =72 steps

The girl will count 72 steps.