Two trains of equal length are running on parallel tracks in the same direction at 36 km/h and 26 km/h. The faster train passes the slower train completely in 36 seconds. What is the length of each train in metres?

Introduction / Context:
Here we have two trains of equal length moving in the same direction at different speeds. The question asks for the length of each train, given the time taken by the faster train to completely overtake the slower one. This problem reinforces the concept of relative speed and the total distance that must be covered in an overtaking situation.

Given Data / Assumptions:

• Speed of faster train = 36 km/h.
• Speed of slower train = 26 km/h.
• Time taken to pass completely = 36 s.
• Lengths of the trains are equal.
• Trains move on parallel tracks with constant speeds.

Concept / Approach:
When one train overtakes another moving in the same direction, the relevant speed is the difference of their speeds. The distance that must be covered is the sum of both train lengths because the faster train needs to completely clear the slower one. Once the relative speed is converted to m/s, the total length is speed times time, and dividing by two gives the length of each train.

Step-by-Step Solution:
Relative speed in km/h = 36 − 26 = 10 km/h. Convert to m/s: 10 * (5 / 18) = 50 / 18 = 25 / 9 m/s. Let L be the length of each train, so total distance for overtaking = 2L. Time for overtaking = 36 s. So, 2L = relative speed * time = (25 / 9) * 36. 2L = (25 / 9) * 36 = 25 * 4 = 100 m. Therefore, L = 100 / 2 = 50 m.

Verification / Alternative check:
Check by substitution: If each train is 50 m, total length = 100 m. At relative speed 25 / 9 m/s, time = 100 / (25 / 9) = 100 * 9 / 25 = 36 s, which matches the given time. This consistency confirms the correctness of the length.

Why Other Options Are Wrong:
Lengths like 24 m, 28 m, or 54 m would produce total lengths of 48 m, 56 m, or 108 m, which do not give a crossing time of 36 s at the given relative speed. Only 50 m leads to the correct time based on the speed difference and overtaking time.

Common Pitfalls:
Learners may forget that for overtaking, the total distance is the sum of both train lengths, not only one length. Another mistake is converting km/h to m/s incorrectly or using the sum of speeds instead of the difference for same direction motion.

Final Answer:
The length of each train is 50 m.