10. (10 points) A ship departs from port $A$ and travels downstream to port $B$ on the same river, then returns upstream to port $A$, taking a total of 3.2 hours; If the distances traveled by the ship in the 1st hour, 2nd hour, and 3rd hour form an arithmetic sequence, and the speed of the current is 2 kilometers per hour; then the total distance traveled by the ship between ports $A$ and $B$ is $\qquad$ kilometers.
【Solution】Solution: The first hour is entirely downstream, similarly, the third hour is entirely upstream, the second hour must be half an hour downstream and half an hour upstream,

Downstream travel time: $1+0.5=1.5$ (hours)
Upstream travel time: $3.2-1.5=1.7$ (hours)
So $V_{\text {down }}: V_{\text {up }}=1.7: 1.5=17: 15$,
$$
\begin{array}{l}
V_{\text {down }}-V_{\text {up }}=2 \times 2=4 \text { (km) } \\
4 \div(17-15) \times 17 \\
=2 \times 17 \\
=34 \text { (km/h) } \\
34 \times 1.5 \times 2 \\
=51 \times 2 \\
=102 \text { (km) }
\end{array}
$$

Answer: The ship travels a total of 102 kilometers between ports $A$ and $B$.
The answer is: 102.