9. (10 points) Given that location $C$ is the midpoint between locations $A$ and $B$. At 7:00 AM, car A departs from $A$ heading towards $B$, while car B and car C depart from $B$ and $C$ respectively, heading towards $A$. When car A and car C meet, car B has completed exactly $\frac{3}{8}$ of the total distance. Car C arrives at $A$ at 10:00 AM, and at 10:30 AM, when car B reaches $A$, car A is still 84 kilometers away from $B$. What is the distance between $A$ and $B$ in kilometers?
【Analysis】First, based on the fact that when A and C meet, they have walked half the total distance, and B has walked $\frac{3}{8}$ of the total distance, we can set up a relationship equation for the speeds of A, B, and C. Then, based on C walking half the distance in 3 hours and B walking the entire distance in 3.5 hours, we can set up another equation for the speed relationship between B and C. The key is to find the speed ratio of A to B. According to the distance from A to B being 84 kilometers, we can determine the corresponding ratio, and thus find the required distance.

【Solution】According to the problem, when A and C meet, they have walked half the total distance, and B has walked $\frac{3}{8}$ of the total distance, i.e., $\frac{3}{4}(V$A $+V_{\text{C}})=V_{\text{B}}$. (1)

Also, C walks half the distance in 3 hours, and B walks the entire distance in 3.5 hours, i.e., $6 V_{\text{C}}=3.5 V_{\text{B}}$. (2)
From (1) and (2), we get: $V_{\text{A}}: V_{\text{B}}=3: 4$. Therefore, the ratio of the distances traveled by A and B is 3:4.
One unit of distance is: $84 \div(4-3)=84$ kilometers.
The total distance is: $84 \times 4=336$ kilometers.
Therefore, the answer is: 336 kilometers.