Multiple choice

Choose the correct answer from the alternatives given. A train 300 m long, passed a man, walking along the line in the same direction at the rate of 3 km/hr in 33 seconds. The speed of the train is

  1. $30 km/hr$
  2. $32 km/hr$
  3. $32\frac{8}{11} \, km/hr$
  4. $35\frac{8}{11} \, km/hr$
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D Correct answer
Explanation

Relative speed = Distance / Time = 300 m / 33 s = 100/11 m/s. Convert to km/hr: (100/11) * (18/5) = 360/11 = 32.7272... km/hr. Since the man is moving in the same direction, Train Speed - Man Speed = 32.7272. Train Speed = 32.7272 + 3 = 35.7272 km/hr, which is 35 and 8/11 km/hr.

AI explanation

Using the relative speed formula for the same direction, convert the man's speed to 5/6 m/s and let the train's speed be x m/s. The relative speed is x minus 5/6 m/s, which equals the 300 m train length divided by 33 seconds, giving 100/11 m/s. Solving for x results in 125/22 m/s, which converts back to km/hr by multiplying by 18/5 to get 1125/22 km/hr. This simplifies to 35 and 8/11 km/hr.

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