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?

We can solve this problem by assigning x as the number of steps were the escalator is standing still. Going up 60 steps means that we must add 60 to x and going down means that we would have to subtract it by x. Since both ways are the same then,

60 + x = 90 - x
x = 15 
Therefore, se would have taken 15 steps to either direction.