"Two towers, one 30 paces and the other 40 paces in height, are 50 paces apart from each other. Between them is a fountain, to which two birds descend at the same moment from the tops of the towers with the same speed and arrive at the same time. What are the horizontal distances from the fountain to the two towers?" (Leonardo of Pisa, Liber Abaci, 1202).

##
In the figure, AD and BC represent the two towers and point E represents the position of the fountain. Since the two birds arrive at the same time, we have $DE = EC$.

Let $x$ be the distance from A to E, and thus $EB = 50 - x$. Using the Pythagorean theorem in triangles DAE and EBC, we have:

$$
\left\{\begin{array}{l}
D E^{2}=30^{2}+x^{2} \\
E C^{2}=40^{2}+(50-x)^{2}
\end{array}\right.
$$

Since DE $= \mathrm{EC}$, we have:

$$
900 + x^{2} = 1600 + 2500 - 100 x + x^{2} \Longleftrightarrow x = 3200 / 100 = 32
$$

Therefore, the horizontal distances from the fountain to the two towers are $AE = x = 32$ steps and $EB = 50 - x = 18$ steps.