Multiple choice

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 travelling 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 directions as the train. What is the length of the train and that of the platform in meters, respectively?

  1. 210 and 140

  2. 162.5 and 187.5

  3. 245 and 130

  4. 175 and 200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Train speed = 54 km/h = 15 m/s. Man speed = 9 km/h = 2.5 m/s. Relative speed (same direction) = 15 - 2.5 = 12.5 m/s. Train length = 12.5 * 14 = 175 m. Time to cross platform = 25s. Total distance = 15 * 25 = 375 m. Platform length = 375 - 175 = 200 m.

AI explanation

The speed of the man is 9 km/h, so the relative speed of the train passing the man running in the same direction is 54 km/h - 9 km/h = 45 km/h. Converting 45 km/h to m/s gives 45 multiplied by 5/18, which equals 12.5 m/s. The time taken to pass the man is 14 seconds, so the length of the train is relative speed multiplied by time, giving 12.5 m/s * 14 s = 175 m. For crossing the platform, the train's actual speed is 54 km/h, which converts to 15 m/s. The total distance covered in 25 seconds is 15 m/s * 25 s = 375 m. Subtracting the train's length from this total distance gives the platform length, which is 375 m - 175 m = 200 m. The length of the train and the platform are 175 m and 200 m, respectively.

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