From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platfor...

Question

From the time the front of a train enters a platform, it takes 25 seconds for the back of the train to leave the platform, while traveling at a constant speed of 54 km/h. At the same speed, it takes 14 seconds to pass a man running at 9 km/h in the same direction as the train. What is the length of the train and that of the platform in meters?

A. 210 and 140  B. 162 and 187.5  C. 245 and 130  D. 175 and 200

Accepted Answer

Train length = 175 m and platform length = 200 m (option D). When a train crosses a platform, the total distance covered equals the train's length plus the platform's length (front enters until back exits). When a train overtakes a man moving in the same direction, the effective relative speed is the difference of their speeds, and the distance covered equals the train's length alone. These two conditions give two equations to solve for the two unknowns.