Express vs local – platform length from combined scenarios A 48 km/h train completely crosses an opposite 42 km/h train (half its length) in 12 s, and passes a platform in 45 s. Find the platform length.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This composite problem first uses relative speed to deduce train length from a crossing event, then applies that length to find a platform length from a single-train crossing time. Handling multiple steps cleanly is the key skill. Given Data / Assumptions: Train A speed = 48 km/h; Train B speed = 42 km/h; B length = A length / 2. They cross (opposite) in 12 s. Train A passes a platform in 45 s at 48 km/h. Concept / Approach:Opposite direction relative speed v_rel = 48 + 42 = 90 km/h = 25 m/s. Crossing time gives sum of lengths. Then use A's platform pass to compute platform length. Step-by-Step Solution: Let length of A be L; of B be L/2.Sum = L + L/2 = 3L/2 = v_rel * 12 = 25 * 12 = 300Thus L = 200 m.For platform: v_A = 48 km/h = 13.333... m/sDistance in 45 s = 13.333... * 45 = 600 mPlatform length = 600 - 200 = 400 m Verification / Alternative check:Recompute crossing: A + B = 200 + 100 = 300 m; 300 / 25 m/s = 12 s, consistent. Why Other Options Are Wrong:450 m, 560 m, 600 m: Do not align with the computed 600 m traverse minus 200 m train length. Common Pitfalls:Using 48 km/h as 48 m/s or forgetting to halve the length of B. Maintain unit discipline. Final Answer:400 m

Express vs local – platform length from combined scenarios A 48 km/h train completely crosses an opposite 42 km/h train (half its length) in 12 s, and passes a platform in 45 s. Find the platform length.

More Questions from Problems on Trains

Discussion & Comments