Multiple choice

Two trains – X and Y, start simultaneously from cities A and B travelling towards each other taking parallel routes. Exactly 8 hours later, they cross each other at city C after which, train X reduces its speed by 12 km/h and train Y increases its speed by 12 km/h, as a result of which, both reach their destinations at the same time. Had there been no changes in the speeds of the trains, considering AB = 864 km, what would have been the difference between the times when the two trains reach their destinations?

  1. 2 hours 48 minutes

  2. 3 hours 24 minutes

  3. 3 hours 36 minutes

  4. 3 hours
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be x and y. They meet at 8 hours, so 8(x+y) = 864, meaning x+y = 108. After meeting, they cover the remaining distance. The time difference is calculated based on the speed change; the total time saved/lost is 3 hours 36 minutes.

AI explanation

Let the initial speeds of train X and Y be x and y. Since they meet after 8 hours, we have 8x + 8y = 864, meaning x + y = 108. The remaining distance for train X is 8y, and for train Y is 8x. After the speed change, train X takes 8y / (x - 12) hours and train Y takes 8x / (y + 12) hours. Because they arrive at the same time, 8y / (x - 12) = 8x / (y + 12). Solving this equation along with x + y = 108 gives x = 60 and y = 48. Without the speed changes, train X's total time would be 864 / 60 = 14.4 hours, and train Y's total time would be 864 / 48 = 18 hours. The difference between these times is 3.6 hours, which is 3 hours and 36 minutes.

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