Agirl wants to count the steps of a moving escalator which is going up. if she is going up on it, she counts 60 steps. if she is walking 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?

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.