Two trains, each 100 m long, moving in opposite directions, cross each other in 8 seconds. If one is moving twice as fast the other, then the speed of the faster train is:

Given Data

• Each train length = 100 m
• They move in opposite directions
• They completely cross each other in 8 s
• One train is twice as fast as the other
• Required: speed of the faster train (km/hr)

Step 1: Relative speed & equationLet slower speed = v m/s ⇒ faster speed = 2v m/s.Opposite directions ⇒ relative speed = v + 2v = 3v m/s.Crossing distance = sum of lengths = 100 + 100 = 200 m.Time = distance ÷ relative speed ⇒ 8 = 200 ÷ (3v)3v = 25 ⇒ v = 25/3 ≈ 8.33 m/s

Step 2: Faster train's speed2v = 50/3 ≈ 16.67 m/sConvert to km/hr: (50/3) × (18/5) = 60 km/hr

Checks & Common Pitfalls

• Use the sum of speeds for opposite directions.
• Use the sum of lengths for complete crossing.
• Convert m/s ↔ km/hr correctly (× 3.6 or × 18/5).

Final AnswerThe faster train's speed is 60 km/hr.