Multiple choice

Two trains each $200$ m long move towards each other on parallel lines with velocities $20$ kmph and $30$ kmph respectively. What is the time that elapses when they first meet until they have cleared each other?

  1. $20$ s
  2. $24.8$ s
  3. $28.8$ s
  4. $30$ s
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Relative speed = 20 + 30 = 50 km/h = 50 * (5/18) m/s = 250/18 m/s. Total distance to cover = 200 + 200 = 400 m. Time = Distance / Speed = 400 / (250/18) = 400 * 18 / 250 = 1.6 * 18 = 28.8 seconds.

AI explanation

To completely cross each other, the total distance to be covered is the sum of their lengths, which is 200 m + 200 m = 400 m. Since the trains are moving towards each other, their relative speed is the sum of their speeds: 20 kmph + 30 kmph = 50 kmph, which converts to 50 x 5/18 = 250/18 m/s. The time taken is calculated by dividing the total distance by the relative speed, giving 400 / (250/18) = 400 x 18 / 250 = 28.8 seconds. The result is 28.8 s.

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