Multiple choice

Two trains of lengths 105 m and 75 m run on parallel lines of rails. While travelling in opposite directions, they pass each other in 18 seconds. When they are running in the same direction at the same speed as before, the faster train passes the other in 36 seconds. Find the speed of the trains in km per hour.

  1. 17 km/hr, 31 km/hr

  2. 9 km/hr, 27 km/hr

  3. 21 km/hr, 36 km/hr

  4. 5 km/hr, 20 km/hr

  5. 15 km/hr, 25 km/hr
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B Correct answer
Explanation

Let speeds be u and v (m/s). (105+75)/(u+v) = 18 => u+v = 10. (105+75)/(u-v) = 36 => u-v = 5. Solving, u = 7.5 m/s, v = 2.5 m/s. Converting to km/hr: 7.5 * 3.6 = 27, 2.5 * 3.6 = 9.

AI explanation

When moving in opposite directions, their relative speed is the sum of their speeds, and the total distance is 180 m, giving the equation u plus v equals 10 m/s. When moving in the same direction, relative speed is the difference of their speeds, giving u minus v equals 5 m/s. Solving these two equations yields speeds of 7.5 m/s and 2.5 m/s, which convert to 27 km/hr and 9 km/hr respectively.

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