Multiple choice

A $150$ metres long train crosses a man walking at the speed of $6$ km/hr in the opposite direction in $6$ seconds. The speed of the train in km/hr is ___________.

  1. $66$
  2. $84$
  3. $96$
  4. $106$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train speed v (m/s). Man speed 6 km/hr = 5/3 m/s. Relative speed = v + 5/3. Distance = 150m. Time = 6s. 150 / (v + 5/3) = 6 implies v + 5/3 = 25, so v = 25 - 1.66 = 23.33 m/s. Convert to km/hr: 23.33 * 18/5 = 84 km/hr.

AI explanation

Using the relative speed formula for opposite directions, divide the 150 meter length by the 6 second crossing time to get a relative speed of 25 m/s. Convert this to km/hr by multiplying by 18/5, resulting in 90 km/hr. Subtracting the man's speed of 6 km/hr from the relative speed gives the train's speed of 84 km/hr.

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