Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:

Given Data

• Each train length = 120 m
• They run in opposite directions with the same speed
• Time to completely cross each other = 12 s
• Required: speed of each train in km/hr

Step 1: Model the crossing using relative speedWhen two trains move in opposite directions, their relative speed = sum of individual speeds.Let the speed of each train = v m/s ⇒ relative speed = 2v m/s.Distance covered to completely cross = sum of lengths = 120 + 120 = 240 m.Use time = distance ÷ speed:12 = 240 ÷ (2v)2v = 240 ÷ 12 = 20 m/sv = 20 ÷ 2 = 10 m/s

Step 2: Convert m/s to km/hr1 m/s = 18/5 km/hrSpeed of each train = 10 × (18/5) = 36 km/hr

Checks & Common Pitfalls

• Use sum of speeds for opposite directions (2v), not v.
• Use sum of lengths for complete crossing (240 m), not a single length.
• Keep units consistent and convert 10 m/s to km/hr by multiplying by 18/5 (or 3.6).

Final AnswerThe speed of each train is 36 km/hr.