Multiple choice

A train passes two persons, walking at the speeds of 2 km/hr and 4 km/hr in the same direction as the train, completely in 9 seconds and 10 seconds, respectively. Calculate the length of the train (in metres).

  1. 54

  2. 45

  3. 50

  4. 72
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let L be length and v be train speed. (v-2) * 5/18 * 9 = L and (v-4) * 5/18 * 10 = L. (v-2) * 2.5 = (v-4) * 2.777. 2.5v - 5 = 2.777v - 11.11. 0.2777v = 6.11, v = 22. L = (22-2) * 5/18 * 9 = 20 * 2.5 = 50.

AI explanation

Let the length of the train be L and its speed be S. Using the relative speed formula for the same direction, we get L equals (S minus 2) multiplied by (5/18) multiplied by 9, and L equals (S minus 4) multiplied by (5/18) multiplied by 10. Equating the two expressions gives 5 multiplied by (S minus 2) equals (50/9) multiplied by (S minus 4), which simplifies to 45S minus 90 equals 50S minus 200, resulting in a train speed of 22 km/h. Substituting this speed back gives the train's length as (22 minus 2) multiplied by (5/18) multiplied by 9, which equals 50 meters.

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