Multiple choice

Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min. Had they been travelling in the same direction, they would have been 32.5 km apart in the same time. Find their speeds (in kmph).

  1. 30, 40

  2. 20, 50

  3. 35, 45

  4. 10, 60
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A Correct answer
Explanation

Let speeds be u and v. Opposite direction: (u+v) * 3.25 = 227.5 => u+v = 70. Same direction: (u-v) * 3.25 = 32.5 => u-v = 10. Solving gives 2u = 80, u = 40; v = 30.

AI explanation

Let the speeds of the two trains be x and y, where x is greater than y. Travelling in opposite directions gives a relative speed of x plus y, so 3 hours 15 minutes multiplied by (x plus y) equals 227.5 km, which simplifies to x plus y equals 70. Travelling in the same direction gives a relative speed of x minus y, so 3.25 hours multiplied by (x minus y) equals 32.5 km, which simplifies to x minus y equals 10. Solving these simultaneous equations gives x equals 40 and y equals 30. The result is 40 kmph and 30 kmph.

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