Multiple choice

Train A left Centerville Station, heading towards Dale City Station, at 3 PM. Train B left Dale City Station, heading toward Centerville Station, at 3:20 PM on the same day. The trains rode on straight tracks that were parallel to each other. If train A travelled at a constant speed of 30 miles per hour and train B travelled at a constant speed of 10 miles per hour, and the distance between Centerville Station and Dale City Station is 90 miles, when did the trains meet each other?

  1. 5:20 pm

  2. 7:20 pm

  3. 5 pm

  4. 7 pm

  5. 9 pm
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A Correct answer
Explanation

Train A starts at 3 PM, speed 30 mph. Train B starts at 3:20 PM, speed 10 mph. By 3:20 PM, Train A has traveled 30 * (20/60) = 10 miles. Remaining distance = 90 - 10 = 80 miles. Relative speed = 30 + 10 = 40 mph. Time to meet = 80 / 40 = 2 hours after 3:20 PM, which is 5:20 PM.

AI explanation

By 3:20 PM, Train A has travelled for 20 minutes at 30 miles per hour, covering a distance of 10 miles and reducing the gap between the trains to 80 miles. The relative speed of the two trains moving towards each other is 40 miles per hour (30 plus 10). They will meet after 80 divided by 40, which is 2 hours, exactly at 5:20 PM.

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