4. The length of the escalator is 200 steps. When Petya walks down the escalator, he manages to count 50 steps. How many steps will he count if he runs twice as fast?
Solution. 80 steps. Let's call the step of the escalator from which Petya begins his descent the first step. When Petya walks down, he passes 50 steps. During this time, the first step manages to descend $200-50=150$ steps. Therefore, the escalator moves three times faster than Petya walks. When Petya runs, the speed ratio will be $3:2$ in favor of the escalator. Thus, Petya will count $200 \cdot 2:(3+2)=80$ steps.