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:

Step 1: Let the speed of the slower train be x m/s.

Then the speed of the faster train = 2x m/s.

Step 2: Both trains are 100 m long and are moving in opposite directions.

Total distance to be covered while crossing = 100 + 100 = 200 meters

Step 3: Relative speed when moving in opposite directions = x + 2x = 3x m/s

Time taken to cross = 8 seconds

Step 4: Apply the formula: distance = speed × time

200 = 3x × 8
=> 3x = 200 / 8 = 25
=> x = 25 / 3 ≈ 8.33 m/s

Step 5: Speed of the faster train = 2x = 2 × 25/3 = 50/3 m/s

Convert to km/hr: (multiply by 18/5)

Speed = (50/3) × (18/5) = 60 km/hr

Answer: 60 km/hr

The speed of the faster train is 60 km/hr.

This is a classic problem involving relative speed when two objects move in opposite directions. The key is to correctly account for their combined length and use the correct conversion factor between m/s and km/hr.