Multiple choice

Two trains can run at a speed of $54$ km/hr and $36$ km/hr on a parallel tracks. When they are running in opposite directions they pass each other in $10$ s, when they move in the same direction a person sitting in the faster train crosses the other train in $30$ s. Find the length of the trains ( faster and slower respectively ).

  1. $100$ m and $150$ m
  2. $150$ m and $100$ m
  3. $150$ m each
  4. $100$ m each
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A Correct answer
Explanation

First, convert the speeds to m/s: 54 km/hr is 15 m/s and 36 km/hr is 10 m/s. When moving in opposite directions, their relative speed is 25 m/s, so the sum of their lengths is 25 * 10 = 250 m. When moving in the same direction, the relative speed is 5 m/s, and the passenger in the faster train takes 30 s to cross the slower train, meaning the length of the slower train is 5 * 30 = 150 m, leaving the faster train's length as 100 m.

AI explanation

The relative speed in opposite directions is (54+36)(5/18) = 25 m/s, so the sum of their lengths is 25 * 10 = 250 m. The relative speed in the same direction is (54-36)(5/18) = 5 m/s, and because a person crosses the slower train, the length of the slower train is 5 * 30 = 150 m. Subtracting this from the total length gives the faster train's length as 250 - 150 = 100 m, making the lengths 100 m and 150 m respectively.

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