A jogger running at 9 kmph alongside a railway track is 240 metres ahead of…

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:

1. Train speed = 45 km/hr, jogger speed = 9 km/hr, both moving in the same direction.

2. Relative (closing) speed = 45 − 9 = 36 km/hr.

3. Convert to m/sec: 36 × 5/18 = 10 m/sec.

4. Total distance to be covered = head-start gap (240 m) + train's own length (120 m) = 360 m.

5. 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.