Multiple choice

A passenger train and a goods train are running in the same direction on parallel railway tracks. If the passenger train now takes three times as long to pass the goods train, as when they are running in opposite directions, then what is the ratio of the speed of the passenger train to that of the goods train? (Assume that the trains run at uniform speeds)

  1. 2 : 1

  2. 3 : 2

  3. 4 : 3

  4. 1 : 1
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A Correct answer
Explanation

Let speeds be P and G. Relative speed opposite = P+G, same = P-G. Time = Distance / Speed. D/(P-G) = 3 * D/(P+G). P+G = 3P-3G => 4G = 2P => P/G = 2/1.

AI explanation

Let the speed of the passenger train be P and the speed of the goods train be G. The time taken to pass each other is proportional to the total distance divided by the relative speed, so for opposite directions the time is proportional to 1 divided by (P plus G). For the same direction, the time is proportional to 1 divided by (P minus G). Since the same direction time is three times the opposite direction time, 1 divided by (P minus G) equals 3 multiplied by 1 divided by (P plus G). Solving this equation gives P plus G equals 3P minus 3G, which simplifies to 2P equals 4G, yielding a ratio of 2 to 1.

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