Multiple choice

Train A crosses a pole in 18 seconds and a platform in 39 seconds. The length of the platform is 157.5 m. If the length of Train B is equal to half the length of Train A plus twice the length of the platform, what is the length of Train B?

  1. 382.5 m

  2. 328.5 m

  3. 238.5 m

  4. 315 m
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A Correct answer
Explanation

Train A length L, speed v. L = v * 18. L + 157.5 = v * 39. Substituting L = 18v: 18v + 157.5 = 39v, so 21v = 157.5, v = 7.5 m/s. L = 18 * 7.5 = 135 m. Train B length = 0.5 * 135 + 2 * 157.5 = 67.5 + 315 = 382.5 m.

AI explanation

Let the train's length be x, so its speed is x/18 and the equation for crossing the platform is 157.5 + x = 39 multiplied by x/18. Solving this gives 2835 + 18x = 39x, meaning the train's length is 2835 divided by 21, which equals 135 meters. The length of Train B is half of 135 plus twice 157.5, which equals 67.5 + 315, resulting in 382.5 meters.

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