A jogger running at 15 km/hr alongside a railway track 280 metres ahead of the…

2025

A jogger running at 15 km/hr alongside a railway track 280 metres ahead of the engine of a 180 metres long train running at 65 km/hr in the same direction. In how much time will the train pass the jogger?

  1. A.

    33.12 sec

  2. B.

    34.56 sec

  3. C.

    35.15 sec

  4. D.

    32.89 sec

Attempted by 6 students.

Show answer & explanation

Correct answer: A

Key steps to solve:

  1. Convert speeds from km/h to m/s.

    Train speed: 65 km/h = 65 × 5/18 = 325/18 m/s ≈ 18.06 m/s.

    Jogger speed: 15 km/h = 15 × 5/18 = 75/18 m/s = 4.1667 m/s.

  2. Find relative speed (train relative to jogger).

    Relative speed = (325/18 − 75/18) = 250/18 = 125/9 m/s ≈ 13.8889 m/s.

  3. Determine the distance the train must cover relative to the jogger for the train to pass completely.

    Initial distance from engine to jogger = 280 m. The train length = 180 m. Total distance = 280 + 180 = 460 m.

  4. Compute time = distance ÷ relative speed.

    Time = 460 ÷ (125/9) = 460 × 9/125 = 4140/125 = 33.12 s (approximately).

Answer: 33.12 sec (approximately).

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