## 81. Escalator.

- Descending on the escalator, I counted 50 steps, - said Walker.
- I counted 75, - objected Trotman, - but I was going down three times faster than you.

If the escalator had stopped, how many steps could be counted on its visible part? It is assumed that both people moved at a constant speed and that the speed of the escalator was constant.
81. Let \(n\) be the number of steps on the escalator; the time it takes for one step to disappear at the bottom, we will take as a unit.

Trotman walks 75 steps in \(n-75\) units of time, or at a speed of 3 steps in \(\frac{n-75}{25}\) units of time. Therefore, Walker covers 1 step in \(\frac{n-75}{25}\) units of time. But he also covers 50 steps in \(n-50\) units of time, or 1 step in \(\frac{n-50}{50}\) units of time. Therefore, \(\frac{n-50}{50}=\frac{n-75}{25}\), from which \(n=100\).