Multiple choice

A train leaves Delhi at 6 am and reaches Agra at 10 am. Another train leaves Agra at 8 am and reaches Delhi at 11:30 am. At what time do the two trains cross each another?

  1. 8:30 am

  2. 8:56 am

  3. 9:26 a.m.

  4. 9 am

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D. Train 1 speed = D/4. Train 2 speed = D/3.5 = 2D/7. Train 1 starts at 6 AM, Train 2 at 8 AM. At 8 AM, Train 1 has traveled D/2. Remaining distance = D/2. Relative speed = D/4 + 2D/7 = (7D+8D)/28 = 15D/28. Time = (D/2) / (15D/28) = 14/15 hours = 56 minutes. 8:00 AM + 56 minutes = 8:56 AM.

AI explanation

Assume the distance is D; the first train takes 4 hours, so its speed is D/4, and the second train takes 3.5 hours, so its speed is D/3.5. By 8 am, the first train has traveled for 2 hours, covering D/2, leaving a remaining distance of D/2 between the trains. Their relative speed is (D/4 plus D/3.5), and the time to meet is the remaining distance divided by this speed, which calculates to approximately 56 minutes, making them cross at 8:56 am.

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