Multiple choice

A man covered a certain distance at some speed. Had he moved $3$ $kmph$ faster he would taken $40$ minutes less. If he had moved $2$ $kmph$ slower, he would have taken $40$ minutes more. The distance in $km$ is:

  1. $35$
  2. $\displaystyle 36\frac{2}{3}$
  3. $\displaystyle 37\frac{1}{2}$
  4. $40$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D and speed be S. D/S - D/(S+3) = 40/60 and D/(S-2) - D/S = 40/60. Solving this system yields S = 12 km/hr and D = 40 km.

AI explanation

Let the original speed be v kmph and the time be t hours. Using the distance formula D = Speed * Time, we get (v + 3)(t - 2/3) = vt and (v - 2)(t + 2/3) = vt. Expanding these gives 3t - 2v/3 = 2 and 2t - 2v/3 = -4/3. Subtracting the second equation from the first yields t = 10/3 hours. Substituting t back into the first equation gives v = 12 kmph. The distance is then 12 * 10/3 = 40 km. The result is 40.

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