Solution:

Draw lines $A$, $B$, $C$, $D$ to graph the movement of the four cars, with time on the $x$-axis and distance on the $y$-axis, and let $(X Y)$ be the point where lines $X$ and $Y$ meet. Then $(A C)$ is the midpoint of the line from $(A B)$ to $(A D)$, and $(D B)$ is the midpoint of the line from $(D A)$ to $(D C)$. Thus, $(B C)$ is the intersection of two medians of the triangle with vertices at $(A B)$, $(A D)$, and $(D C)$, so it is the centroid. But this means the distance from $(A C)$ to $(B C)$ is half the distance from $(B C)$ to $(C D)$. Since $A$ meets $C$ at 9 am and $C$ meets $D$ at $2 \mathrm{pm}$, the time between these meetings is 5 hours. The meeting of $C$ and $B$ occurs $1/3$ of the way from the first meeting to the second, i.e. $5/3$ hours after $A$ meets $C$, or at 10:40am.