Multiple choice

A train covered a certain distance at a uniform speed. If the train would have been $6:km/h$ faster, it would have taken $4$ hours less than the scheduled time. And, if the train were slower by $6: km/h$, it would have taken $6$ hours more than the scheduled time. Find the length of the journey.

  1. The length of the journey is $400\:km$.
  2. The length of the journey is $650\:km$.
  3. The length of the journey is $500\:km$.
  4. The length of the journey is $720\:km$.
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D Correct answer
Explanation

Let distance be D and speed be S. D/S - D/(S+6) = 4 and D/(S-6) - D/S = 6. Solving these equations yields S=30 and D=720.

AI explanation

Using the standard train speed and time equation, we let the initial speed be v, the scheduled time be t, and the distance be d. The conditions give 6t - 6v = 24 and 6v + 6t = 36 from the provided differences. Adding these two equations gives 12t = 60, so t = 5 hours. Multiplying by 12 yields v = 30 km/h, making the total journey distance 30 multiplied by 24 hours, which equals 720 km.

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