A kid is walking up a downward-moving escalator with a constant speed and counts 72 stairs. Then the kid walks down with the same speed and now counts 36 stairs. Being confused, the kid waits until the mall closes and the escalator is still, so he now walks up the escalator with half the speed he had before. How many stairs did he count?

Total number of steps = steps climbed oneself + steps produced by escalator, so:

Let the kid's speed be $v$. Let the speed of the escalator be $u$. So in the two cases: $$72-72\dfrac{u}{v} = 36+36\dfrac{u}{v} $$ so $$\dfrac{u}{v} = \dfrac{1}{3}$$

So the total number of stairs at any given moment are 48, right?

Now how do we answer the last question?

How does his speed affect the number of stairs he counted?