Multiple choice

Two trains Doronto Express and Toronto Express of lengths 200 m and 260 m are moving at speeds of 54 kmph and 72 kmph are running on parallel tracks in opposite directions, respectively. They enter a 300 m long tunnel at the same time. Which train exits the tunnel first and how much length of the other train was still in the tunnel?

  1. Toronto Express, 100 m

  2. Doronto Express, 90 m

  3. Toronto Express, 80 m

  4. Doronto Express, 80 m

  5. Toronto Express, 90 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Speeds in m/s: 54 kmph = 15 m/s, 72 kmph = 20 m/s. Time to clear tunnel: Doronto (200m train + 300m tunnel) = 500/15 = 33.33s. Toronto (260m train + 300m tunnel) = 560/20 = 28s. Toronto exits first. In 28s, Doronto has traveled 28 * 15 = 420m. Since the tunnel is 300m long, the front of the Doronto train has already exited, but the back is still in the tunnel. The length of Doronto inside the tunnel is 200 - (420 - 300) = 80m.

AI explanation

To find the time to exit the tunnel, use the formula time equals total distance divided by speed. For Doronto Express, the time to cross the tunnel is the sum of its length and tunnel length divided by its speed in meters per second: (200 + 300) divided by (54 multiplied by 5/18), which is 500 divided by 15, or 33.33 seconds. For Toronto Express, the time is (260 + 300) divided by (72 multiplied by 5/18), which is 560 divided by 20, or 28 seconds, meaning Toronto Express exits first. In the remaining 5.33 seconds (160/3 seconds minus 28 seconds), Doronto Express travels 15 multiplied by 16/3, which equals 80 meters, leaving 420 meters still inside; since the tunnel is 300 meters long, there are 80 meters of the train still in the tunnel.

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