A train travelling at a speed of 60 km/hr crosses a platform in 20 seconds. The same train crosses a person who is walking at a speed of 6 km/hr in the same direction as that of the train in 12 seconds. What is the length of the train and that of the platform, respectively?

To find the train's length, we use the relative speed when it overtakes the person. The train's speed is 60 km/hr and the person's speed is 6 km/hr in the same direction, resulting in a relative speed of 54 km/hr (60 - 6). Converting this to m/s: 54 * (5/18) = 15 m/s. The train crosses the person in 12 seconds, so the train length is 15 m/s * 12 s = 180 m. Next, to find the platform length, we use the train's actual speed of 60 km/hr, which is 60 * (5/18) = 16.67 m/s. In 20 seconds, the train covers a total distance (train + platform) of 16.67 * 20 = 333.33 m. Subtracting the train's length (180 m) from the total distance gives the platform length: 333.33 - 180 = 153.33 m.