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The image contains the following mathematical problem:

"Two trains start at \( A \) and \( B \) and move to and fro between \( A \) and \( B \) at speeds of 90 km/h and 70 km/h, respectively. If \( AB = 400 \) km, find the time after which they meet each other."

### Solution:

1. **Understanding the Problem:**
   - Train 1 departs from point \( A \) and travels at a speed of 90 km/h.
   - Train 2 departs from point \( B \) and travels at a speed of 70 km/h.
   - The distance between \( A \) and \( B \) is 400 km.

2. **Relative Speed:**
   - Since the trains are moving towards each other, their relative speed is the sum of their individual speeds:
     \[
     \text{Relative speed} = 90 \text{ km/h} + 70 \text{ km/h} = 160 \text{ km/h}
     \]

3. **Time to Meet:**
   - The time taken for the trains to meet each other can be found using the formula:
     \[
     \text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{400 \text{ km}}{160 \text{ km/h}} = 2.5 \text{ hours}
     \]

### Final Answer:
The trains will meet after **2.5 hours**.

Would you like to explore further details or have any questions on this topic?

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Here are some related questions you might find interesting:

1. How would the solution change if one train was delayed by 30 minutes?
2. What if the distance \( AB \) was increased to 500 km?
3. How would the meeting time change if both trains had the same speed?
4. Can you determine the meeting point distance from \( A \) given the speeds and distance?
5. How does the relative speed concept apply in scenarios with different units of measure?
6. What if there was a third train starting from \( A \) after a delay? How would it affect the meeting time?
7. How can you apply this problem-solving technique to other areas, such as physics or economics?
8. What assumptions are made in this problem, and how would the solution change if they were different?

**Tip:** Always check whether trains (or objects in similar problems) are moving towards or away from each other, as it significantly affects the calculation of the relative speed.

Explore how to calculate the time at which two trains, starting from points A and B, meet when traveling towards each other at speeds of 90 km/h and 70 km/h respectively over a distance of 400 km. Learn the concepts of relative speed and apply basic algebra to solve the problem.

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