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This problem involves two cars, denoted as \( 甲 \) and \( 乙 \), starting from points \( A \) and \( B \) respectively, moving towards each other. The problem asks for the distance between \( A \) and \( B \).

### Given:
1. The first meeting happens 60 km away from \( A \).
2. After the first meeting, they return to their starting points and meet again, 40 km away from \( A \).

### Analysis:

Let the distance between \( A \) and \( B \) be \( D \).

1. **First Meeting:**
   - Car \( 甲 \) travels 60 km to the meeting point.
   - Car \( 乙 \) travels \( D - 60 \) km to the same meeting point.
   - The ratio of their speeds is \( \frac{60}{D-60} \).

2. **Second Meeting:**
   - After the first meeting, they return to their respective starting points.
   - They meet again 40 km away from \( A \).
   - Car \( 甲 \) travels \( D + 40 \) km before the second meeting.
   - Car \( 乙 \) travels \( 2D - (D + 40) = D - 40 \) km before the second meeting.
   - The ratio of their speeds is also \( \frac{D + 40}{D-40} \).

Since the ratios of their speeds must be the same in both cases:

\[
\frac{60}{D - 60} = \frac{D + 40}{D - 40}
\]

### Solving the Equation:

Cross-multiplying gives:

\[
60 \times (D - 40) = (D - 60) \times (D + 40)
\]

Expanding both sides:

\[
60D - 2400 = D^2 - 60D + 40D - 2400
\]

Simplifying:

\[
60D - 2400 = D^2 - 20D - 2400
\]

Cancelling out the \(-2400\) terms and moving all terms to one side:

\[
D^2 - 80D = 0
\]

Factoring out \( D \):

\[
D(D - 80) = 0
\]

Thus, \( D = 80 \) km.

### Conclusion:

The distance between points \( A \) and \( B \) is **80 km**.

Would you like a more detailed explanation, or do you have any other questions? Here are five related questions:

1. What would the solution be if the meeting points were different distances from \( A \)?
2. How would the problem change if the cars were traveling at different speeds?
3. What if the cars met at the midpoint between \( A \) and \( B \) first?
4. How can we determine the speeds of the cars given this scenario?
5. What assumptions are we making about the cars' motion in this problem?

**Tip:** When dealing with problems involving relative motion, setting up ratios of distances and speeds can simplify finding unknowns.

Learn how to solve the problem of calculating the distance between points A and B when two cars start from these points and travel towards each other. Detailed step-by-step solution provided. Suitable for high school students studying distance and speed problems.

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