Multiple choice

A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?

  1. 3 km

  2. 4 km

  3. 5 km

  4. 2 km
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A Correct answer
Explanation

Train A speed = 45 kmph = 12.5 m/s. Train B speed = 81 kmph = 22.5 m/s. Relative speed = 35 m/s. In 4s, distance covered = 35 * 4 = 140m. Length A + Length B = 140. Since B = 0.5A, 1.5A = 140, A = 93.33m. Train A passes tunnel in 4 min (240s). Distance = Speed * Time = 12.5 * 240 = 3000m = 3km. Length of tunnel = 3000 - 93.33 = 2.9km, which is approx 3km.

AI explanation

First, convert the speeds of Train A and Train B to metres per second by multiplying by 5 over 18, giving 12.5 metres per second and 22.5 metres per second respectively. Their relative speed is 12.5 plus 22.5, equaling 35 metres per second, and since they pass each other in 4 seconds, the sum of their lengths is 35 multiplied by 4, equaling 140 metres. Because Train B is half the length of Train A, the length of Train A is 140 multiplied by 2 over 3, giving approximately 93.33 metres. Converting Train A's speed of 45 kmph to 0.75 kilometres per minute, the tunnel length is 0.75 multiplied by 4 minutes minus 0.093 kilometres, resulting in approximately 2.9 kilometres, which rounds to 3 kilometres.

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