Multiple choice

Train A is running at a speed of 36 km/hr and crosses a man who is running at a speed of 6 km/hr in the same direction as the train in 6 sec. Another train B of length 490 m is running at a speed of 54 km/hr in the opposite direction. Find the time taken by train A to cross train B.

  1. 45.4 sec

  2. 50 sec

  3. 21.6 sec

  4. 40 sec

  5. 65.6 sec
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Train A speed = 10 m/s. Man speed = 1.66 m/s. Relative speed = 8.33 m/s. Length of A = 8.33 * 6 = 50 m. Total distance to cross B = 50 + 490 = 540 m. Relative speed (opposite) = 10 + 15 = 25 m/s. Time = 540 / 25 = 21.6 sec.

AI explanation

First, find the length of train A by using the formula for relative speed in the same direction: length equals relative speed multiplied by time. The relative speed is 36 kmph minus 6 kmph, which equals 30 kmph, or 25/3 meters per second. Multiplying this by 6 seconds gives the length of train A as 50 meters. When train A crosses train B moving in the opposite direction, their relative speed is the sum of their speeds: 36 plus 54, resulting in 90 kmph, which converts to 25 m/s. The total distance to cross is the sum of their lengths, 50 plus 490, which equals 540 meters. Dividing the total distance by the relative speed gives the time: 540 divided by 25 equals 21.6 seconds.

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