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 hrs less than the scheduled time. And, if the train were slower by 6 km/h, it would have taken 6 hrs more than the scheduled time. Find the distance covered by the train.

  1. 180 kms

  2. 360 kms

  3. 720 kms

  4. None of these
Reveal answer Fill a bubble to check yourself
C 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: D(6)/(S(S+6)) = 4 => 3D = 2S(S+6). D(6)/(S(S-6)) = 6 => D = S(S-6). Substitute D: 3S(S-6) = 2S(S+6) => 3S - 18 = 2S + 12 => S = 30. Then D = 30(30-6) = 30 * 24 = 720.

AI explanation

Using the formula distance equals speed multiplied by time, we establish two equations based on the constant distance: (x + 6)(y - 4) = xy and (x - 6)(y + 6) = xy, where x is the usual speed and y is the usual time. Expanding and simplifying these equations yields the system 3x - 2y = 12 and 2x - y = 12. Solving this system gives a speed of 30 km/h and a time of 24 hours, making the total distance 30 * 24 = 720 kms.

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