Two trains are running in opposite directions in the same speed. The length of…

Concept

When two objects move in opposite directions, their relative speed is the sum of their individual speeds. When two trains cross each other completely, the total distance covered equals the sum of both train lengths, and this full distance is covered in the given time at that relative speed.

Application

1. Total distance covered while the trains cross each other = length of first train + length of second train = 120 m + 120 m = 240 m.

2. Time taken to cross each other = 12 s.

3. Let the speed of each train be v m/s. Since the trains move in opposite directions, their relative speed = v + v = 2v.

4. Relative speed = total distance ÷ time = 240 ÷ 12 = 20 m/s, so 2v = 20 m/s.

5. Speed of each train, v = 20 ÷ 2 = 10 m/s.

6. Convert to km/hr: speed in km/hr = speed in m/s × 18/5 = 10 × 18/5 = 36 km/hr.

Cross-check

Converting the relative speed directly: 20 m/s × 18/5 = 72 km/hr. Since both trains contribute equally to this relative speed, one train's own speed is half of 72 km/hr, i.e. 36 km/hr — the same result obtained above.