Let's solve the problem in the image step by step:

Problem:

Two trains leave stations A and B towards each other at the same time with speeds of 50 km/h and 60 km/h, respectively. When they meet, the second train has traveled 120 km more than the first train. We need to find the distance between the two stations (A and B).

Solution:

1. Let the distance traveled by the first train be $x$ km.

   • Then, the distance traveled by the second train will be $x + 120$ km (since the second train has traveled 120 km more than the first).

2. Time of travel for both trains is the same (since they meet at the same time).

   • Using the formula for time: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
   • Time for the first train: $\frac{x}{50}$
   • Time for the second train: $\frac{x + 120}{60}$
   • Since the time is equal: $\frac{x}{50} = \frac{x + 120}{60}$

3. Solve for $x$: $\frac{x}{50} = \frac{x + 120}{60}$ Cross-multiply: $60x = 50(x + 120)$ Expand: $60x = 50x + 6000$ Simplify: $60x - 50x = 6000$ $10x = 6000$ $x = 600$

4. Find the total distance between A and B:

   • The distance between the two stations is the sum of the distances traveled by both trains: $\text{Total Distance} = x + (x + 120)$
   • Substitute $x = 600$: $\text{Total Distance} = 600 + (600 + 120)$ $\text{Total Distance} = 600 + 720 = 1320 \, \text{km}.$

Final Answer:

The distance between stations A and B is 1320 km.

Do you want a deeper explanation of any step? Here are some follow-up questions to consider:

1. How is the equation for time equality derived?
2. Why is time equal for both trains when they meet?
3. How do speeds and relative distances influence the total distance in this problem?
4. Could we solve this problem using relative speed? How?
5. How can we verify that the solution is correct?

Tip:

Always use the concept of time equality when solving problems where two objects meet after starting at the same time. This ensures consistency in equations.