Two passenger trains start at the same time from two different stations and move towards each other at 16 km/h and 21 km/h respectively. When they meet, one train has travelled 60 km more than the other. What is the distance between the two stations?

Introduction / Context:
This is a distance and relative motion problem involving two trains travelling towards each other at different speeds. The extra piece of information that one train travels 60 km more than the other at the meeting point allows us to set up a simple linear equation to find their travel time and then compute the total distance between stations.

Given Data / Assumptions:

• Speed of first train = 16 km/h.
• Speed of second train = 21 km/h.
• They start at the same time from two different stations.
• They move towards each other on a straight route.
• At the meeting point, one train has travelled 60 km more than the other.

Concept / Approach:
If both trains travel for the same time t hours until they meet, distances covered are 16t and 21t. The faster train naturally covers more distance. According to the problem, the difference between these distances is 60 km. So we can write 21t − 16t = 60, solve for t, and then compute the total distance between stations as the sum of the distances travelled by both trains.

Step-by-Step Solution:
Let t = time in hours until the trains meet. Distance travelled by slower train = 16t. Distance travelled by faster train = 21t. Given that the faster train travels 60 km more: 21t − 16t = 60. 5t = 60 → t = 60 / 5 = 12 hours. Distance by slower train = 16 * 12 = 192 km. Distance by faster train = 21 * 12 = 252 km. Total distance between stations = 192 + 252 = 444 km.

Verification / Alternative check:
We can verify that the difference between 252 km and 192 km is indeed 60 km as required. Also, the total distance 444 km divided by the combined speed (16 + 21 = 37 km/h) gives time 444 / 37 = 12 hours, which matches our value of t. Both checks confirm that the calculations are consistent.

Why Other Options Are Wrong:
Distances such as 387 km, 242 km, or 145 km do not satisfy both the total distance and the 60 km difference condition when combined with speeds of 16 km/h and 21 km/h. Using these distances with the given speeds would produce either a different time or a different difference in distances, so they cannot be correct.

Common Pitfalls:
A common error is to misinterpret the 60 km difference as the total distance instead of the difference, or to forget that both trains travel for the same time t. Another mistake is to try to apply relative speed directly without using the extra difference information correctly. Setting up a clear equation for distance difference is the safest method.

Final Answer:
The distance between the two stations is 444 km.