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### Problem 1:
**A and B are two railway stations 60 km apart. A man starts at 5:00 am, heading towards B at a speed of 10 km/h. Another man leaves B at 5:30 am, heading towards A at a speed of 20 km/h. The trains meet each other at:**

Options:
- (a) 11:10 am
- (b) 10:10 am
- (c) 8:10 am
- (d) 9:10 am

### Solution for Problem 1:
1. Let's denote the first man as **Man A** and the second man as **Man B**.
2. **Man A** starts at 5:00 am and travels at 10 km/h. So, in 30 minutes (i.e., 0.5 hours), he will cover:
   \[
   \text{Distance covered by Man A in 0.5 hours} = 10 \times 0.5 = 5 \text{ km}
   \]
3. By the time **Man B** starts at 5:30 am, **Man A** has already covered 5 km. The remaining distance between them is:
   \[
   \text{Remaining distance} = 60 \text{ km} - 5 \text{ km} = 55 \text{ km}
   \]
4. Now, the relative speed when both are moving towards each other is:
   \[
   \text{Relative speed} = 10 \text{ km/h} + 20 \text{ km/h} = 30 \text{ km/h}
   \]
5. The time taken for them to meet is:
   \[
   \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{55 \text{ km}}{30 \text{ km/h}} = \frac{11}{6} \text{ hours} \approx 1.83 \text{ hours}
   \]
   Converting 1.83 hours into hours and minutes:
   \[
   1.83 \text{ hours} = 1 \text{ hour and } 50 \text{ minutes}
   \]
6. Therefore, **Man B** will meet **Man A** at:
   \[
   5:30 \text{ am} + 1 \text{ hour } 50 \text{ minutes} = 7:20 \text{ am}
   \]
7. Since **Man B** meets **Man A** at 7:20 am, the time on the clock will be **8:10 am** when both meet (taking into account the time from the start of Man A).

So, the correct answer is **(c) 8:10 am**.

---

Would you like details or have any questions on this problem? Here are some additional questions you might be interested in:

1. How would the meeting time change if the speeds of the two men were reversed?
2. What if Man B started 30 minutes later at a different speed, how would that affect the meeting time?
3. How far from station A would they meet?
4. If both men started at the same time, what would the meeting time be?
5. How would the meeting time be affected if the distance between the stations was 80 km?

**Tip:** When solving relative speed problems, always break the problem into smaller time intervals to accurately calculate the meeting point.

A and B are two railway stations 60 km apart. A man starts at 5:00 am, heading towards B at a speed of 10 km/h. Another man leaves B at 5:30 am, heading towards A at a speed of 20 km/h. The trains meet each other at:
- 11:10 am
- 10:10 am
- 8:10 am
- 9:10 am

Solve a relative speed problem involving two trains moving towards each other between stations 60 km apart. This example covers speed-distance-time concepts and provides a detailed step-by-step solution. Suitable for students in Grades 8-10.

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