Multiple choice

Two trains 200$\mathrm { m }$ and 150$\mathrm { m }$ long are running on parallel rails at the rate of 40$\mathrm { kmph }$ and 45$\mathrm { kmph }$ respectively. In how much time will they cross each other, if they are running in the same direction?

  1. 72$\mathrm { sec }$
  2. 132$\mathrm { sec }$
  3. 192$\mathrm { sec }$
  4. 252$\mathrm { sec }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speed = 45 - 40 = 5 km/hr = 5 * (5/18) m/s = 25/18 m/s. Total distance = 200 + 150 = 350 m. Time = Distance / Speed = 350 / (25/18) = 350 * 18 / 25 = 14 * 18 = 252 seconds.

AI explanation

Because the trains are running in the same direction, use the relative speed formula by subtracting their speeds, which gives 45 kmph minus 40 kmph equals 5 kmph. Convert this relative speed to metres per second by multiplying by 5/18, resulting in 25/18 m/s. The total distance to be covered for the trains to cross each other is the sum of their lengths, giving 200 m plus 150 m equals 350 m. Divide the total distance of 350 m by the relative speed of 25/18 m/s to get the time of 252 seconds.

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