A jogger running at 9 kmph alongside a railway track in 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?

Step 1: Convert speeds from km/h to m/s

Speed of train = 45 km/h = (45 × 1000) / 3600 = 12.5 m/s
Speed of jogger = 9 km/h = (9 × 1000) / 3600 = 2.5 m/s

Step 2: Find the relative speed

Since both are moving in the same direction, subtract the jogger’s speed from the train’s speed.

Relative speed = 12.5 - 2.5 = 10 m/s

Step 3: Total distance to be covered to completely pass the jogger

The jogger is 240 meters ahead, and the train is 120 meters long. So, the train has to cover:

Distance = 240 + 120 = 360 meters

Step 4: Time to pass the jogger

Time = Distance / Relative Speed = 360 / 10 = 36 seconds

Answer: 36 seconds

The train will take 36 seconds to pass the jogger completely.

This is a classic example of a relative speed problem where both the train and the person are moving in the same direction. Understanding relative motion is crucial for solving such questions accurately in time-based aptitude exams.