The correct answer is option (C):
624 km
Here's the breakdown of how to solve this classic relative motion problem:
1. **Understand Relative Speed:** When two objects move towards each other, their speeds combine to determine how quickly they close the distance between them. In this case, the trains are approaching each other. Their relative speed is the sum of their individual speeds: 36 kmph + 42 kmph = 78 kmph.
2. **Analyze the Distance Difference:** The problem states that one train traveled 48 km more than the other when they met. This difference in distance is a key piece of information.
3. **Relate Distance, Speed, and Time:** The fundamental formula we'll use is: distance = speed x time.
4. **Consider the Time:** Both trains start at the same time and travel until they meet. Therefore, they travel for the same amount of time. Let's call this time 't' hours.
5. **Set Up Equations:**
* Let 'd1' be the distance traveled by the first train (at 36 kmph).
* Let 'd2' be the distance traveled by the second train (at 42 kmph).
* We know: d2 - d1 = 48 km (one train moved 48 km more)
* We also know: d1 = 36t and d2 = 42t
6. **Solve for Time (t):**
* Substitute the distance equations into the distance difference equation: 42t - 36t = 48
* Simplify: 6t = 48
* Solve for t: t = 8 hours
7. **Calculate the Total Distance (Distance between A and B):**
* The total distance between A and B is the sum of the distances traveled by both trains: d1 + d2.
* d1 = 36 * 8 = 288 km
* d2 = 42 * 8 = 336 km
* Total Distance = 288 km + 336 km = 624 km
Therefore, the distance between stations A and B is 624 km.