2. Petya climbed up a moving upward escalator, counting 75 steps, and then descended the same escalator (i.e., moving against the direction of the escalator), counting 150 steps. During the descent, Petya walked three times faster than during the ascent. How many steps are there on the stopped escalator?
Answer: 120.

For convenience, let's introduce a unit of time during which Petya took one step while ascending the escalator. We will measure all speeds in steps per unit of time. Petya's speed while ascending is 1 step per unit of time, and his speed while descending is 3 steps per unit of time. Let the speed of the escalator be $x$. The absolute speed of Petya was $1+x$ while ascending and $3-x$ while descending. Petya spent 75 units of time ascending and 50 units of time descending (he took steps three times faster while descending). The distance covered while ascending and descending was the same - the length of the escalator. Therefore, $75 \cdot(1+x)=50 \cdot(3-x)$, from which $125 x=75, x=0.6$.

The length of the escalator is $75 \cdot(1+0.6)=120$ steps. This is the number of steps on the stopped escalator.