Multiple choice

A train overtakes two persons walking along a railway track. The first one walks at $4.5$ km/hr. The other one walks at $5.4$ km/hr. The train needs $8.4$ and $8.5$ seconds, respectively, to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?

  1. $81$ km/hr
  2. $82$ km/hr
  3. $83$ km/hr
  4. $84$ km/hr
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A Correct answer
Explanation

Let train speed be v (km/hr). Relative speeds are (v - 4.5) and (v - 5.4). Convert to m/s: (v - 4.5) * 5/18 and (v - 5.4) * 5/18. Distance = speed * time. Train length L = (v - 4.5) * (5/18) * 8.4 = (v - 5.4) * (5/18) * 8.5. (v - 4.5) * 8.4 = (v - 5.4) * 8.5. 8.4v - 37.8 = 8.5v - 45.9. 0.1v = 8.1. v = 81 km/hr.

AI explanation

Let the train's length be L and speed be S; converting the walking speeds to m/s gives 1.25 m/s and 1.5 m/s. Setting up the relative speed equations gives S - 1.25 = L / 8.4 and S - 1.5 = L / 8.5. Solving these equations, we find L = 168 m and S = 22.5 m/s, which converts to 81 km/hr.

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