Problems based on Trains
Time taken to cross each other
1. When a train, crosses telephone post or a tree, the train will move a distance equal to the length of the train.
∴ Time taken by train to cross a telephone post
| = | Length of train | ||
| Speed of train |
2. When a train crosses a bridge or a platform the train will have to travel a distance equal to the sum of the lengths of the bridges and the train.
∴ Time taken by the train to cross a platform
| = | Length of train + Length of Platform | ||
| Speed of train |
3. If two trains a and b are running in the same direction, then the relative speed of the faster train a with respect to the slower train 'b' is the difference between the speeds of the faster train 'a' and the slower train 'b'.
Then, the time in which the trains will cross each other is the time taken by the faster train. 'a' covering a distance equal to the sum of the lengths of the train with respect to the relative speed.
∴ Time taken by solver train to catch the faster train
| = | Distance covered in extra time | ||
| Difference in their speeds |
Time taken to cross each other
| = | Sum of the lengths of both trains | ||
| Difference in their speeds |
4. If two trains are running in opposite directions, then the relative speeds of the faster train a with respect to the slower train b is the sum of the speeds.
5. When a train crosses a man who is walking two situation arises.
Case I : When the train and man are moving in the same direction, then the relative speed of the train with respect to the speed of the man = Speed of train - Speed of man
The time taken by train to cross the man will be the time taken by moving a distance equal to the length of the train with respect of the relative speed.
Case II : The train and man move at the same time in the opposite directions. Then, the relative speed of the train with respect to the Speed of man will be = Speed of the train + Speed of the man
Time taken by the train to crossing the man will be the same as the time taken in moving a distance equal to the length of the train with respect to the relative speed.
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