Máté is always in a hurry. He noticed that standing on the moving staircase, he reaches the metro in half a minute, while on the stationary staircase, he can descend in 1 minute. How long will it take Máté to reach the bottom if he can run down the moving staircase?
Let $s$ denote the length of the moving staircase in meters. Máté's speed standing on the moving staircase (i.e., the speed of the staircase's movement): $v_{1}=\frac{s}{1.5} \mathrm{~m} / \mathrm{min}$, on the stationary staircase $v_{2}=\frac{s}{1} \mathrm{~m} / \mathrm{min}$. If both the staircase and Máté are moving, their speeds add up. Since it is a uniform motion,

$$
t=\frac{s}{v}=\frac{s}{v_{1}+v_{2}}=\frac{s}{\frac{2 s}{3}+s}=\frac{3}{5} \text{ min}
$$

Máté can descend the moving staircase in 36 seconds. Kardos Dániel (Szombathely, Kanizsai D. Gymn., 8th grade)