A jogger runs at 9 km/h alongside a railway track and is 240 m ahead of the engine of a 120 m long train that is moving in the same direction at 45 km/h. In how many seconds will the train completely pass the jogger?

Introduction / Context:
This train and jogger question checks understanding of relative speed in the same direction and the idea that a train must cover both the initial gap and its own length to completely pass a moving person. It is a common pattern in competitive exam aptitude sections on trains and distances.

Given Data / Assumptions:

• Speed of jogger = 9 km/h.
• Speed of train = 45 km/h.
• Length of train = 120 m.
• Jogger is initially 240 m ahead of the train engine.
• Both move in the same direction at constant speeds.

Concept / Approach:
The train must first close the 240 m gap between the engine and the jogger, and then cover its own length of 120 m to pass completely. Since both move in the same direction, effective relative speed is the difference of their speeds. We convert this relative speed into metres per second and use time = distance / speed to find the time taken to pass the jogger.

Step-by-Step Solution:
Step 1: Relative speed in km/h = 45 - 9 = 36 km/h. Step 2: Convert 36 km/h to m/s using factor 5/18. Step 3: Relative speed = 36 * 5 / 18 = 10 m/s. Step 4: Total distance to be covered relative to jogger = initial gap + train length = 240 + 120 = 360 m. Step 5: Use time = distance / speed, so time = 360 / 10 = 36 seconds.

Verification / Alternative check:
We can check by seeing how far each moves in 36 seconds. Train distance = 10 m/s relative speed * 36 s = 360 m compared to jogger, which matches the required distance 360 m. This shows that the front of the train reaches and then fully clears the jogger in 36 seconds at the given speeds.

Why Other Options Are Wrong:

• 10 seconds: At 10 seconds, the relative distance covered is only 100 m, which is less than the 360 m needed.
• 48 seconds: This would give 480 m of relative motion, which is beyond the required distance.
• 56 seconds: This is even longer and gives a relative distance of 560 m, which is not consistent with the described situation.

Common Pitfalls:
One common mistake is to consider only the 240 m gap and forget that the whole length of the train must clear the jogger. Another error is to add speeds incorrectly or fail to convert km/h to m/s. Some learners also confuse relative distance with absolute distance along the track, so it is important to think carefully in terms of positions relative to the jogger.

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