Multiple choice

Two trains, A and B, run at speeds 81 km/h and 36 km/h, respectively. They take 32 seconds less to cross each other when they run in opposite directions as compared to the time they take to cross each other when they run in the same direction. Also, the length of train A is 80 m less than the length of train B. Find the length of train A.

  1. 350 m

  2. 200 m

  3. 365 m

  4. 285 m

  5. 280 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Relative speeds: opposite = 81+36=117 km/h (32.5 m/s), same = 81-36=45 km/h (12.5 m/s). Let lengths be L and L+80. Time = (L1+L2)/Speed. (2L+80)/12.5 - (2L+80)/32.5 = 32. Solving for L gives 285.

AI explanation

Let the length of train B be L; the length of train A is then L minus 80. Their relative speed in opposite directions is 81 plus 36, or 117 km/h, which converts to 65/2 m/s; their relative speed in the same direction is 81 minus 36, or 45 km/h, converting to 25/2 m/s. Using the time difference of 32 seconds, we set up the equation (2L minus 80) divided by 25/2 minus (2L minus 80) divided by 65/2 equals 32. Solving this equation gives L equal to 365 meters. Since the length of train A is 80 meters less than train B, its length is 365 minus 80, which is 285 meters.

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