Multiple choice

A train takes 20 seconds to cross a platform of length 400 meters and 16 seconds to cross a man running in the direction opposite to that of the train with a speed of 5 m/s. How long does the train take to cross a pole?

  1. 40 3 seconds

  2. 15 seconds

  3. 25 seconds

  4. 50 3 seconds
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D Correct answer
AI explanation

When crossing the platform, the total distance is the train's length plus the platform's length, so 12v equals the train's length plus 400. When passing the man running in the opposite direction, their relative speed is v + 5, and the distance is just the train's length, so the train's length equals 16(v + 5). Substituting the second equation into the first gives 12v = 16v + 80 + 400, which simplifies to 4v = -480, yielding a speed of 120 meters per second. The time to cross a pole is the train's length divided by v. The train's length is 16(120 + 5) = 2000 meters. The time taken is 2000 / 120, which equals 50 / 3 seconds.

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