Multiple choice

Train A leaves from P to Q. Half an hour later train B leaves for P from Q. Two hours after A had started, the trains meet. A has covered 50 % more distance than train B when they meet. What is the ratio of the speeds of train A to train B?

  1. $9:8$
  2. $8:9$
  3. $5:7$
  4. $8:3$
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A Correct answer
Explanation

Let speed of A be Va and B be Vb. A travels for 2 hours, B travels for 1.5 hours. Distance Da = 2Va, Db = 1.5Vb. Da = 1.5 * Db => 2Va = 1.5 * 1.5Vb => 2Va = 2.25Vb => Va/Vb = 2.25/2 = 9/8.

AI explanation

Train A travels for 2 hours, while train B travels for 1.5 hours before they meet. Since train A covers 50 percent more distance than train B, the ratio of their distances is 3 to 2. Using distance equals speed multiplied by time, 2 times the speed of A equals 1.5 times the speed of B, making the ratio of their speeds 9 to 8.

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