14. Little Marco goes up and down from one floor to another on the escalator of a shopping center, one step at a time. If he proceeds in the direction of the escalator's movement at a constant speed relative to it (i.e., the time interval between steps is constant), he steps on 15 steps. If he proceeds in the opposite direction (with the same time interval between steps), he steps on 35. How many steps would Marco step on when passing from one floor to another if the escalator were stationary?
14. The answer is 21. Let $V_{s}$ be the speed of the escalator, in steps per unit of time, and $V_{m}$ be Marco's speed, in the same unit of measurement. If $T_{1}$ and $T_{2}$ are, respectively, the times Marco takes to travel the escalator in the concordant direction and in the discordant direction, then the following relationships hold

$$
\begin{array}{r}
\left(V_{m}+V_{s}\right) T_{1}=N \\
\left(V_{m}-V_{s}\right) T_{2}=N \\
V_{m} \cdot T_{1}=15 \\
V_{m} \cdot T_{2}=35
\end{array}
$$

where $N$ is the number of steps Marco would step on if the escalator were stationary. From equations (1) and (2), it follows that

$$
\frac{T_{1}}{T_{2}}=\frac{N-15}{35-N}
$$

while from equations (3) and (4), it follows that

$$
\frac{T_{1}}{T_{2}}=\frac{15}{35}
$$

Combining the two relationships (5) and (6) obtained, we get

$$
N=\frac{2 \cdot 15 \cdot 35}{15+35}=21
$$

which is exactly the harmonic mean of the numbers 15 and 35.