Multiple choice

The rails on a railroad are $30\ m$ long. As the train passes over the point where the rails are joined, there is an audible click. The speed of the train in km per hour is approximately the number of clicks heard in

  1. $108\ seconds$
  2. $2\ minutes$
  3. $1\dfrac {1}{2} minutes$
  4. $5\ minutes$

  5. None of these
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A Correct answer
Explanation

Let speed be v km/hr. v km/hr = v * (1000/3600) m/sec = v * (5/18) m/sec. Time per rail = 30 / (v * 5/18) = 30 * 18 / 5v = 108/v seconds. If the number of clicks is N, then time = N * (108/v). The question implies N = v, so time = v * (108/v) = 108 seconds.

AI explanation

Let the train's speed be x km/hr, which converts to 5x/18 m/s. The time to travel one 30 m rail is 30 divided by 5x/18, which simplifies to 108/x seconds. This means the number of clicks heard directly equals the numerical speed in km/hr in a time of 108 seconds.

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