## 10. Escalator in the Metro

Usually, I go up the escalator in the metro. I calculated that when I walk up the stairs of the moving upward escalator, I climb 20 steps myself, and the entire ascent takes me exactly $60 \mathrm{c}$. My wife walks up the stairs more slowly and only climbs 16 steps; therefore, the total time she spends on the ascent is longer - it takes her 72 seconds.

How many steps would I have to climb if the escalator suddenly breaks down?
10. Let $x$ be the unknown number of steps on the stationary escalator. When the escalator is working, it rises at a speed of $x-20$ steps in 60 seconds (this follows from calculations related to my ascent) or at a speed of $x-16$ steps in 72 seconds (which follows from how my wife ascends). Thus, the speed of the escalator's movement is $[(x-16)-(x-20)]$ in 12 seconds (72-60). Therefore, in 60 seconds, the escalator moves up 20 steps. From this, it follows that the full span of the escalator contains 20 plus 20 steps, i.e., a total of 40 steps.