Two trains of the same length take 6 s and 9 s, respectively, to cross a pole. If both trains run in the same direction, how long (in seconds) will they take to completely cross each other?

Introduction / Context:
Time to cross a pole gives L/v for each train (L being the common length). With same-direction motion during crossing, relative speed is the difference of speeds, and the distance to be covered is the sum of the lengths (2L).

Given Data / Assumptions:

• Train 1: L/v1 = 6 s ⇒ v1 = L/6
• Train 2: L/v2 = 9 s ⇒ v2 = L/9
• Same direction ⇒ relative speed = v1 − v2

Concept / Approach:
Crossing time T = (2L) / (v1 − v2) = 2L / (L/6 − L/9) = 2 / (1/6 − 1/9).

Step-by-Step Solution:

Verification / Alternative check:
Set L = 18 arbitrary units ⇒ v1 = 3, v2 = 2; 2L = 36 distance; relative speed = 1 ⇒ time = 36 s ✔

Why Other Options Are Wrong:

• 30, 40, 42 s do not satisfy the ratio implied by 6 s and 9 s single-pole times.

Common Pitfalls:

• Using sum of speeds for same direction instead of difference.

Final Answer:
36 s