Two trains are running in the same direction at 30 km/h and 58 km/h respectively. A man sitting in the slower train takes 18 seconds to completely pass the faster train. What is the length (in metres) of the faster train?

Introduction / Context:
This question again involves relative speed, but now both trains are moving in the same direction and a person is sitting in the slower train. The man sees the faster train pass by, which effectively measures how long it takes to cross the length of the faster train at the relative speed between the two trains.

Given Data / Assumptions:

• Speed of slower train = 30 km/h.
• Speed of faster train = 58 km/h.
• Direction of motion: same direction.
• Time for a man in slower train to pass the faster train = 18 seconds.
• The man's speed equals the speed of the slower train.

Concept / Approach:
In the frame of the man, the faster train appears to move past him at the relative speed between the two trains, which is their speed difference when they move in the same direction. The distance that needs to be covered relative to the man is the length of the faster train. Thus, length of faster train = relative speed * time, using m/s for the speed.

Step-by-Step Solution:
Relative speed = 58 - 30 = 28 km/h. Convert 28 km/h to m/s: 28 * 1000 / 3600 = 28 * 5 / 18 = 140 / 18 = 7.777... m/s. Time taken to pass faster train = 18 seconds. Length of faster train = relative speed * time. Length ≈ 7.777... * 18 = 140 m.

Verification / Alternative check:
Compute exactly using fraction: relative speed = 28 * 1000 / 3600 = 700 / 90 = 70 / 9 m/s. Multiply by 18 s: (70 / 9) * 18 = 70 * 2 = 140 m. This confirms the length of the faster train is exactly 140 m.

Why Other Options Are Wrong:

• 105 m, 115 m and 120 m are all smaller and do not satisfy length = (70 / 9) * 18 when recalculated.

Common Pitfalls:
Some candidates add the speeds instead of subtracting them, which is correct only when trains move in opposite directions. Others forget the unit conversion from km/h to m/s, leading to serious calculation errors. It is also important to realise that the entire length of the faster train must pass the observer for the crossing to be complete.

Final Answer:
The length of the faster train is 140 m.