16. (15 points) Person A and Person B start climbing a mountain from the bottom along the same path at the same time, and immediately return along the original path after reaching the top. It is known that their descending speeds are three times their respective ascending speeds. A and B meet 150 meters below the summit, and when A returns to the bottom, B is exactly halfway down the mountain. Find the distance from the bottom to the top of the mountain.
【Solution】Solution one: When they meet 150 meters away from the mountaintop, the distance difference between the two is 200 meters,
the speed ratio of A to B is 8:7,
thus, A's uphill distance is $\frac{200}{2-1} \times 8=1600$,
of these 1600 meters, 50 meters are the result of assuming continued uphill travel,
therefore, the distance from the mountain bottom to the mountaintop $=1600-50=1550$ meters.
Solution two: Let A's uphill speed be $x$, then the downhill speed is $3 x$. B's uphill speed is $y$, then the downhill speed is $3 y$, and the distance from the mountaintop to the mountain bottom is $s$.
$$
\left\{\begin{array}{l}
\frac{s}{x}+\frac{150}{3 x}=\frac{s-150}{y} \text { (1) } \\
\frac{s}{x}+\frac{s}{3 x}=\frac{s}{y}+\frac{0.5 s}{3 y} \text { (2) }
\end{array},\right.
$$

From (1) we get $\frac{s+50}{s-150}=\frac{x}{y}$,
$$
\begin{array}{l}
\text { From (2) we get } \frac{x}{y}=\frac{8}{7}, \\
\therefore \frac{s+50}{s-150}=\frac{8}{7}, \\
\therefore s=1550 \text { (meters), }
\end{array}
$$

In conclusion, the answer is 1550 meters.