Two trains A and B are moving from two opposite points of a Town X and Y respectively. Distance between X and Y is 392km. Train B moves with a speed of 16 km/h and starts its journey at 8.00 am in the morning. Train A moves with a speed of p km/h and starts its journey at 10.00 am in the morning. They meet at 8.00 pm in the same day for the first time. What is the approximate distance of their second meeting point from X?

To solve this problem, we first need to determine the speed \( p \) of Train A and then use that to find the distance of their second meeting point from point X.

### Step 1: Time taken for the first meeting
- Train B starts at 8:00 AM and travels until 8:00 PM, so the time taken by Train B is 12 hours.
- Train A starts at 10:00 AM and travels until 8:00 PM, so the time taken by Train A is 10 hours.

### Step 2: Calculate the distance covered by Train B
The distance covered by Train B can be calculated as:
\[
\text{Distance covered by Train B} = \text{Speed of Train B} \times \text{Time taken by Train B} = 16 \, \text{km/h} \times 12 \, \text{hours} = 192 \, \text{km}
\]

### Step 3: Distance covered by Train A until the first meeting
Let \( p \) be the speed of Train A. The distance covered by Train A until the first meeting is:
\[
\text{Distance covered by Train A} = p \times 10 \, \text{hours} = 10p \, \text{km}
\]

### Step 4: Determine the speed \( p \) of Train A
Since the total distance between X and Y is 392 km, the sum of the distances covered by both trains until they meet is equal to 392 km:
\[
192 \, \text{km} + 10p \, \text{km} = 392 \, \text{km}
\]
\[
10p = 392 - 192 = 200
\]
\[
p = \frac{200}{10} = 20 \, \text{km/h}
\]

### Step 5: Time taken for the second meeting
Since Train A and Train B meet for the second time, the distance between X and Y will be covered by the sum of their speeds in a certain amount of time. The total time for the second meeting can be calculated by using the relative speed and distance.

Total speed when they are moving towards each other:
\[
\text{Relative speed} = p + 16 = 20 + 16 = 36 \, \text{km/h}
\]
Total distance:
\[
\text{Time for one full meeting} = \frac{392}{36} \, \text{hours} \approx 10.89 \, \text{hours}
\]

### Step 6: Distance covered by Train A in 10.89 hours
Now, considering that Train A starts moving from X and moves for another 10.89 hours until the second meeting:
\[
\text{Distance covered by Train A from X to the second meeting point} = 20 \times 10.89 \approx 217.8 \, \text{km}
\]

### Final Answer
The approximate distance of their second meeting point from X is **217.8 km**.

Would you like more details or have any further questions?

### Related Questions:
1. What would happen if Train A started at 8:00 AM as well?
2. How would the time of the first meeting change if Train B’s speed increased?
3. If the distance between X and Y was doubled, how would that affect the second meeting point?
4. What if Train B started 2 hours later than it actually did?
5. How would the problem change if Train A's speed was reduced by 4 km/h?

### Tip:
When working with problems involving relative speed, always account for the time difference in the start of the journeys.

Explore how to solve a problem involving two trains, A and B, starting from opposite points X and Y. Learn about speed, distance, and time calculations. Suitable for high school students.

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