Multiple choice

Two trains, running at the speeds of 49 kmph and 37 kmph on parallel rails in opposite directions, are observed to pass each other in 9 seconds. When they are running in the same direction at the same speeds as before, a person sitting in a train observes that he passes the other train in 45 seconds. Find the lengths of the two trains.

  1. 175 m, 55 m

  2. 150 m, 65 m

  3. 165 m, 50 m

  4. 115 m, 100 m

  5. None of these
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B Correct answer
AI explanation

When the trains travel in opposite directions at 49 kmph and 37 kmph, their relative speed is 86 kmph, which converts to 430 over 18 m/s, giving the sum of their lengths as 430 over 18 times 9, or 215 m. When traveling in the same direction, the relative speed is 12 kmph, which converts to 10 over 3 m/s. The observation that a person passes the other train in 45 seconds gives a relative distance of 10 over 3 times 45, which equals 150 m, meaning the train the person is on is 150 m long. The other train's length is 215 minus 150, which gives lengths of 150 m and 65 m.

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