2. (10 points) Car A departs from $A$ heading towards $B$, traveling back and forth; Car B departs from $B$ at the same time heading towards $A$, traveling back and forth. After the two cars meet for the first time, Car A continues to drive for 4 hours to reach $B$, and Car B continues to drive for 1 hour to reach $A$. If the distance between $A$ and $B$ is 100 kilometers, then when Car A first reaches $B$, Car B's position is $\qquad$ kilometers away from $A$.
【Analysis】Let the speed of car A be $v_{1}$, and the speed of car B be $v_{2}$. According to the ratio of distances traveled being equal to the ratio of speeds, we can derive the distance ratio of the two cars at the first meeting. Then, based on the fact that after the first meeting, car A continues to travel for 4 hours to reach $B$, and car B continues to travel for 1 hour to reach $A$, we can calculate the distances traveled by the two cars. Since the distances are exchanged, we can then find the ratio of the speeds, and based on the ratio of the speeds, we can determine the distance traveled by car B when car A first reaches $B$, which gives us the distance of car B from $A$.

【Solution】Solution:
Let the speed of car A be $v_{1}$, and the speed of car B be $v_{2}$.
As shown in the figure, the first meeting occurs at point $C$, then
$$
\frac{\mathrm{AC}}{\mathrm{BC}}=\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}},
$$

and $A C=v_{2}, B C=4 v_{1}, \frac{\mathrm{v}_{2}}{4 \mathrm{v}_{1}}=\frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}, v_{2}=2 v_{1}$,
Therefore, when car A first reaches $B$, car B is at point $B$, 100 kilometers away from $A$.
The answer is: 100.