Multiple choice

Two trains are moving in the same directions on a parallel track at the speed of 42 km/hr and 60 km/hr. The first train passes a man standing on a platform in 6 sec while the second train passes the man in 9 sec. In what time do the trains cross each other?

  1. 43 sec

  2. 44 sec

  3. 46 sec

  4. 48 sec
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train 1 speed = 42 km/h = 42 * 5/18 = 35/3 m/s. Length 1 = (35/3) * 6 = 70 m. Train 2 speed = 60 km/h = 60 * 5/18 = 50/3 m/s. Length 2 = (50/3) * 9 = 150 m. Relative speed = 60 - 42 = 18 km/h = 5 m/s. Time to cross = (70 + 150) / 5 = 220 / 5 = 44 sec.

AI explanation

The lengths of the trains are found using the formula distance equals speed times time, with the first train's speed of 42 km/hr converting to 35/3 m/s to give a length of 6 multiplied by (35/3) equals 70 m. The second train's speed is 60 km/hr or 50/3 m/s, giving a length of 9 multiplied by (50/3) equals 150 m. Their relative speed moving in the same direction is (60 minus 42) equals 18 km/hr, which is 5 m/s, so the total distance of 220 m divided by 5 m/s gives a crossing time of 44 sec.

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