Multiple choice

Two trains X and Y start at the same time in the opposite direction from two points P and Q and arrive at their destinations 36 and 25 hours respectively after their meeting each other. At what speed does the second train Y travel if the first train travels at 80 km/h.

  1. 80 km/hr

  2. 90 km/hr

  3. 70 km/hr

  4. 96 km/hr

  5. 60 km/hr
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D Correct answer
Explanation

For two objects meeting and then reaching destinations in t1 and t2 time, the ratio of speeds is v1/v2 = sqrt(t2/t1). 80/v2 = sqrt(25/36) = 5/6. v2 = 80 * 6 / 5 = 96 km/h.

AI explanation

According to the rule that if two trains start simultaneously from opposite directions, the ratio of their speeds is the square root of the inverse ratio of the times they take to reach their destinations after crossing each other. This gives the speed of train Y divided by 80 equals the square root of 36 divided by 25. Simplifying this, the speed of train Y divided by 80 equals 6 divided by 5. Solving for the speed of train Y gives 96 km/hr.

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