A train travelling at 60 km/h catches up with a slower train travelling in the same direction. From the moment it draws level with the slower train, it leaves the slower train 120 metres behind in 18 seconds. What is the speed of the slower train in km/h?

Introduction / Context:
This question deals with a faster train overtaking a slower train moving in the same direction. It tests understanding of relative speed in the same direction and how to convert a relative distance gained over a known time into the difference between speeds. From this, the speed of the slower train can be determined.

Given Data / Assumptions:

• Speed of faster train = 60 km/h.
• Trains move in the same direction on parallel tracks.
• In 18 seconds, after drawing level, the faster train is 120 metres ahead of the slower train.
• The distance gained relative to the slower train in that time is 120 metres.
• We must find the speed of the slower train in km/h.

Concept / Approach:
When two objects move in the same direction, the relative speed is the difference between their speeds. The relative distance covered in a certain time is equal to this relative speed multiplied by the time. Here, the faster train gains 120 metres on the slower one in 18 seconds, so the relative speed in metres per second is 120 / 18. We then convert that relative speed into km/h and subtract it from the speed of the faster train to obtain the speed of the slower one.

Step-by-Step Solution:
Step 1: Relative distance gained = 120 metres in 18 seconds.Step 2: Relative speed in metres per second = 120 / 18 = 20 / 3 metres per second.Step 3: Convert relative speed to km/h using 1 metre per second = 18 / 5 km/h.Step 4: Relative speed in km/h = (20 / 3) * 18 / 5 = (20 * 18) / (3 * 5) = 360 / 15 = 24 km/h.Step 5: Let speed of slower train be v km/h. Then 60 - v = 24, so v = 60 - 24 = 36 km/h.

Verification / Alternative check:
If the slower train runs at 36 km/h, then the speed difference = 60 - 36 = 24 km/h.Convert 24 km/h to metres per second: 24 * 5 / 18 = 20 / 3 metres per second.In 18 seconds, distance gained = (20 / 3) * 18 = 120 metres, which matches the question statement.

Why Other Options Are Wrong:
Values like 42 km/h or 44 km/h result from arithmetic mistakes when converting units or manipulating equations. The option 72 km/h is larger than the speed of the faster train and is impossible. A slower train speed of 48 km/h gives a relative speed of only 12 km/h, which does not produce a gain of 120 metres in 18 seconds.

Common Pitfalls:
Some learners treat the distance 120 metres as the length of a train rather than the relative distance gained, leading to a different setup. Others forget to convert between metres per second and km/h or use the wrong factor 5 / 18 instead of 18 / 5 at the wrong step. Carefully distinguishing between absolute and relative motion and checking unit consistency prevent such errors.

Final Answer:
The speed of the slower train is 36 km/h.