**Important Concepts and Formulas**

**Time taken to cross a man or pole –**

Length of Train / Speed of Train

**Time taken to cross a Platform –**

Length of (Train + platform) to Speed of Train

**Time taken to cross a Bridge –**

Length of (Train + platform) to Speed of Train

**When two trains move towards each other, then the time taken to cross each other is –**

Ratio of ** Sum of Lengths of both Trains** to

*the Sum of their Speeds***When two trains are moving in the same direction, then the time taken to cross each other is –**

Ratio of ** Sum of Lengths of both Trains** to the

*Difference of their Speeds***Relative Speeds**

- When two trains @ x km/hr and y km/hr respectively move towards each other-

**Relative Speed = (x + y) km/hr**

- When two trains @ x km/hr and y km/hr respectively move in the same direction-

**Relative Speed = (x – y) km/hr**

__Example-__

__Example-__

**Q- 1> A train 150 meters long is running with a speed of 68 kmph. At what time will it pass a man who is running at 8 km/hr in the same direction in which the train is moving?**

**Solution-**

Relative Speed – (68 – 8) kmph = 60 kmph

Speed in m/sec = 60 × 5/18 = (50/3) m/sec

Now, Time taken by the train to cross the man is the time taken by the train to cover 150-meter distances.

So, Time = (Distance / Speed) = (150 × 3)/50 = 9 seconds (Answer)