## 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-

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)