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?

Given Data

• Speed of train = 45 kmph
• Speed of jogger = 9 kmph
• Initial gap between train front and jogger = 240 m
• Length of train = 120 m

Step 1: Convert speeds to m/s Use 1 kmph = (1000/3600) m/s = (5/18) m/s Train speed = 45 × (5/18) = 12.5 m/s Jogger speed = 9 × (5/18) = 2.5 m/s

Step 2: Relative speed (same direction) Relative speed = Train speed − Jogger speed = 12.5 − 2.5 = 10 m/s

Step 3: Total distance the train must cover relative to the jogger To completely pass the jogger, the front of the train must first close the 240 m gap and then the entire train length (120 m) must go past the jogger. Total relative distance = 240 + 120 = 360 m

Step 4: Time = Distance ÷ Relative speed Time = 360 ÷ 10 = 36 seconds

Sanity Check (in kmph units) Relative speed = 36 kmph. Distance = 0.36 km. Time = 0.36 ÷ 36 hour = 0.01 hour = 36 seconds.

Final Answer The train will pass the jogger in 36 seconds.