Multiple choice

A train X takes 2 hours less than a train Y to cover a distance of 192 km between two cities. Their average speeds differ by 16 km/hr. How long does the faster train take to cover the journey?

  1. 3 hours

  2. 4 hours

  3. 5 hours

  4. 6 hours
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B Correct answer
Explanation

Let speed of Y be v, then speed of X is v + 16. Time taken: 192/v - 192/(v+16) = 2. Simplifying: 192(v+16-v) = 2v(v+16) => 96 * 16 = v^2 + 16v => v^2 + 16v - 1536 = 0. Solving gives v = 32. Faster train X speed = 48. Time = 192/48 = 4 hours.

AI explanation

Let the time taken by the faster train be t hours, making the slower train's time (t + 2) hours. Since both trains cover 192 km, their speeds are 192/t and 192/(t + 2). The difference in their speeds is 16 km/hr, so 192/t - 192/(t + 2) = 16. Multiplying by t(t + 2) gives 192t + 384 - 192t = 16t^2 + 32t, which simplifies to 16t^2 + 32t - 384 = 0. Dividing by 16 yields t^2 + 2t - 24 = 0, which factors to (t - 4)(t + 6) = 0. Since time must be positive, the faster train takes 4 hours.

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