7. (6 points) Cars A and B depart from locations $A$ and $B$ respectively at the same time and travel towards each other. Car A travels at 40 kilometers per hour, and Car B travels at 60 kilometers per hour. After reaching $B$ and $A$ respectively, they immediately return. On the return trip, Car A's speed increases by one half, while Car B's speed remains unchanged. It is known that the distance between the two points where the two cars meet for the second time is 50 kilometers. What is the distance between $A$ and $B$ in kilometers?
【Analysis】Given that car A originally travels 40 kilometers per hour and car B travels 60 kilometers per hour, the speed ratio of the two cars is 40: $60=2: 3$. When they meet for the first time, car A has traveled $\frac{2}{2+3}=\frac{2}{5}$ of the total distance, and car B has traveled $\frac{3}{2+3}=\frac{3}{5}$. After car A accelerates, its speed is $60 \times\left(1+\frac{1}{2}\right)=60$ kilometers per hour, meaning the two cars have the same speed on their return trip. When car A reaches point B, car B, being faster, has already started its return trip. Since car A has completed the entire journey, car B has traveled $\frac{3}{2}$ of the distance car A has traveled, which means car B has traveled an additional $\frac{3}{2}-1=\frac{1}{2}$ of the total distance from point A. With the same speed, each travels half the remaining distance, meeting $\frac{1}{4}$ of the distance from point B. Therefore, the 50 kilometers represents $\frac{3}{5}-\frac{1}{4}=\frac{7}{20}$ of the total distance, so the total distance is $50 \div \frac{7}{20}$ kilometers.

【Solution】The speed ratio of car A and car B is: $40: 60=2: 3$. After car A accelerates, its speed is $60 \times\left(1+\frac{1}{2}\right)=60$ kilometers per hour.
$$
\begin{array}{l}
\left(\frac{3}{2}-1\right) \div 2=\frac{1}{4} \\
50 \div\left(\frac{3}{2+3}-\frac{1}{4}\right) \\
=50 \div\left(\frac{3}{5}-\frac{1}{4}\right) \\
=50 \div \frac{7}{20} \\
=\frac{1000}{7} \text { (kilometers) }
\end{array}
$$

Answer: The distance between the two places is $\frac{1000}{7}$ kilometers.
The answer is: $\frac{1000}{7}$.