463. From two ports A and B, two steamships set off simultaneously towards each other across the sea. The speed of each is constant. The first steamship arrived at B 16 hours after the meeting, while the second arrived at A 25 hours after the meeting. How long does it take for each steamship to travel the entire distance?
$\triangle$ Let the path AB be a unit. Denote the speeds of the steamships as $v_{1}$ and $v_{2}$ (in fractions of a unit per hour).

Suppose the steamships met at point C. Then $\frac{A C}{C B}=\frac{v_{1}}{v_{2}}$. From this,

$$
\frac{A C}{C B}+1=\frac{v_{1}}{v_{2}}+1, \quad \frac{1}{C B}=\frac{v_{1}+v_{2}}{v_{2}}, \quad C B=\frac{v_{2}}{v_{1}+v_{2}}, \quad A C=\frac{v_{1}}{v_{1}+v_{2}}
$$

Since the first steamship traveled the path CB in 16 hours, and the second steamship traveled the path CA in 25 hours, then

$$
\left\{\begin{array}{l}
\frac{v_{2}}{\left(v_{1}+v_{2}\right) v_{1}}=16 \\
\frac{v_{1}}{\left(v_{1}+v_{2}\right) v_{2}}=25
\end{array}\right.
$$

Solving this system of equations, we determine $v_{1}$ and $v_{2}: v_{1}=\frac{1}{36}, v_{2}=\frac{1}{45}$.

Therefore, the time for the steamships to complete the entire path is

$$
1: \frac{1}{36}=36(h), \quad 1: \frac{1}{45}=45(h)
$$

Answer: 36 h, 45 h.