Multiple choice

A train X travelling at 60 km/h overtakes another train Y, 225 m long, and completely passes it in 72 seconds. If the trains had been going in opposite directions, they would have passed each other in 18 seconds. The length (in m) of X and the speed (in km/h) of Y respectively are:

  1. 245 and 54

  2. 245 and 45

  3. 255 and 36

  4. 255 and 40
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let X length = L, speed = S. Relative speed (same direction) = S - Y_speed = (L + 225) / 72. Relative speed (opposite) = S + Y_speed = (L + 225) / 18. (S+Y)/(S-Y) = 72/18 = 4. S+Y = 4S - 4Y => 3S = 5Y. S = 60 km/h = 60 * 5/18 = 50/3 m/s. 3 * (50/3) = 5Y => Y = 10 m/s = 36 km/h. L+225 = (S-Y) * 72 = (60-36) * 5/18 * 72 = 24 * 5/18 * 72 = 24 * 20 = 480. L = 480 - 225 = 255.

AI explanation

When moving in opposite directions, the relative speed is 18 times the sum of the lengths, and when moving in the same direction, it is 72 times the sum. Let the total length be D and the opposite relative speed be S. From the opposite direction case, D = 18S. Substituting this into the same direction case gives 72 = 18S divided by (60 - V), where V is the speed of train Y. This reveals that the opposite relative speed is four times the same direction relative speed, meaning S = 4(60 - V). Using the given length of Y and the equations, the length of X is 255 m and the speed of Y is 36 km/h.

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