Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is (M.A.T., 2003)

### Concept & Relative Speed (Same Direction) When two bodies move in the same direction, their relative speed is the difference between their individual speeds. The total distance covered when one train passes another is the sum of their lengths. $$Relative\ Speed = S_{faster} - S_{slower}$$ $$Total\ Distance = L_1 + L_2$$ ### Step-by-Step Solution 1. **Given:** Speeds are 46 km/hr and 36 km/hr. Time to pass = 36 seconds. Let the length of each train be $L$. 2. Total distance to cover = $L + L = 2L$. 3. Calculate relative speed: $46 - 36 = 10$ km/hr. 4. Convert relative speed to m/s: $$10 \times \frac{5}{18} = \frac{50}{18} = \frac{25}{9}\ m/s$$ 5. Set up the distance equation: $Distance = Speed \times Time$. $$2L = \frac{25}{9} \times 36$$ 6. Solve for $L$: $$2L = 25 \times 4$$ $$2L = 100$$ $$L = 50\ meters$$ ### Exam Strategy & Shortcut Relative speed is 10 kmph. In 36 seconds, the distance covered is $10 \times (5/18) \times 36 = 100$ meters. Since both trains have equal length, this distance represents twice the length of one train. $100 / 2 = 50$ m. ### Common Pitfall Forgetting to divide the total distance by 2. Students often calculate the total distance (100 m) and select it as the answer, forgetting that the question asks for the length of *each* train. ### Final Answer Therefore, the correct answer is **50 m**.