A jogger running at 9 kmph alongside a railway track is 240 metres ahead of…
2025
A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
- A.
3.6 sec
- B.
18 sec
- C.
36 sec
- D.
72 sec
Attempted by 7 students.
Show answer & explanation
Correct answer: C
Concept: When two objects move in the SAME direction, the rate at which the gap between them closes (the relative/closing speed) is the DIFFERENCE of their speeds, not the sum. For a train to completely pass a point object that already has a head start, the train must cover a total distance equal to that head-start gap plus its own length, since the rear of the train has to draw level with the object.
Application:
Train speed = 45 km/hr, jogger speed = 9 km/hr, both moving in the same direction.
Relative (closing) speed = 45 − 9 = 36 km/hr.
Convert to m/sec: 36 × 5/18 = 10 m/sec.
Total distance to be covered = head-start gap (240 m) + train's own length (120 m) = 360 m.
Time = Distance / Speed = 360 / 10 = 36 seconds.
Cross-check: Working entirely in km and hours as an independent check: distance = 0.36 km, relative speed = 36 km/hr, so time = 0.36/36 hr = 0.01 hr = 0.01 × 3600 = 36 seconds. Both methods agree.
So the train takes 36 seconds to pass the jogger.