Trains X and Y leave station A at 6:30 a.m. and 7:40 a.m. respectively and travel in the same direction at 30 km/h and 40 km/h. How many kilometres from station A will the two trains meet?

Introduction / Context:
This is another chase problem involving two trains leaving the same station at different times and different speeds. It checks the ability to compute head start distance, relative speed, and then translate the time of meeting into distance from the starting point.

Given Data / Assumptions:

• Train X leaves station A at 6:30 a.m. at 30 km/h.
• Train Y leaves station A at 7:40 a.m. at 40 km/h.
• Both trains travel in the same direction on the same route.
• We need the distance from station A where they meet.
• Speeds remain constant and trains do not stop.

Concept / Approach:
First, compute how long Train X travels before Train Y starts, and convert that time into a head start distance. Then find the relative speed between the trains, treating it as a chase. Using relative speed, determine how long Train Y takes to catch Train X. Finally, multiply the total time Train X has been travelling by its speed to get the distance from station A where they meet.

Step-by-Step Solution:
Time gap between departures = 7:40 a.m. − 6:30 a.m. = 1 hour 10 minutes = 7/6 hours. Head start distance of Train X = 30 * (7/6) = 35 km. Relative speed = 40 − 30 = 10 km/h. Time taken by Train Y to close the 35 km gap = 35 / 10 = 3.5 hours. Total time Train X travels until meeting = 7/6 + 3.5 = 7/6 + 7/2 = 14/3 hours. Distance from A at meeting point = 30 * (14/3) = 140 km.

Verification / Alternative check:
We can also compute from Train Y perspective. Train Y travels for 3.5 hours at 40 km/h, covering 140 km. This matches the distance we obtained from the perspective of Train X, so both views are consistent. Therefore the meeting point is 140 km from station A.

Why Other Options Are Wrong:
Distances like 96 km, 120 km, or 142 km do not satisfy the time and speed relationships. For example, 120 km would require different travel times from each perspective that conflict with the calculated head start and relative speed, so they cannot be correct meeting distances for the data given.

Common Pitfalls:
A common mistake is to ignore the delayed start of Train Y and assume both start together. Another frequent issue is mis-converting 1 hour 10 minutes into fractional hours. Handling time carefully and using relative speed correctly ensures an accurate solution.

Final Answer:
The two trains will meet at a point 140 km from station A.