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Two trains of equal lengths take 12 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 300 meters, in what time (in seconds) will they cross each other travelling in opposite direction?

Question

Two trains of equal lengths take 12 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 300 meters, in what time (in seconds) will they cross each other travelling in opposite direction?

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Solution

To solve this problem, we first need to find the speed of each train.

  1. Speed is given by the formula Speed = Distance/Time. Here, the distance is the length of the train and the time is the time it takes to cross the post.

  2. For the first train, Speed = 300m/12s = 25 m/s.

  3. For the second train, Speed = 300m/15s = 20 m/s.

  4. When two trains are moving in opposite directions, their relative speed is the sum of their individual speeds. So, the relative speed of the two trains = 25 m/s + 20 m/s = 45 m/s.

  5. Now, when two trains cross each other, the total distance to be covered is the sum of the lengths of the two trains. Since the trains are of equal length, the total distance = 300m + 300m = 600m.

  6. Time is again given by the formula Time = Distance/Speed. So, the time taken for the two trains to cross each other = 600m / 45 m/s = 13.33 seconds.

So, the two trains will cross each other in 13.33 seconds when travelling in opposite directions.

This problem has been solved

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