Multiple choice

The distance between two stations A and B is 900 km. A train starts from A and moves towards B at an average speed of 30 km/hr. Another train starts from B, 20 minutes earlier than the train at A, and moves towards A at an average speed of 40 km/hr. How far from A will the two trains meet ?

  1. 380km

  2. 320km

  3. 240km

  4. 330km

  5. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let t be the time in hours the train from A travels. The train from B travels for t + 1/3 hours (20 minutes = 1/3 hour). Distance = 30t + 40(t + 1/3) = 900. Solving gives 70t + 40/3 = 900, so 70t = 2660/3, t = 38/3 hours. Distance from A = 30 * (38/3) = 380 km.

AI explanation

The train starting from B travels for 20 minutes at 40 km/hr, covering 40 * (1 / 3) = 13.33 km. The remaining distance between the two trains is 900 - 13.33 = 886.67 km. Their relative speed is 30 + 40 = 70 km/hr, so they meet after 886.67 / 70 = 12.666 hours. The train from A travels 30 * 12.666 = 380 km from A.

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