Multiple choice

A man covered a certain distance on a scooter. Had he moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. The distance (in km) was

  1. 20

  2. 36

  3. 37.5

  4. 40
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let distance be D and speed be v. D/v - D/(v+3) = 40/60 = 2/3. Also D/(v-2) - D/v = 40/60 = 2/3. Solving these equations: D/v - D/(v+3) = D/(v-2) - D/v. 2/v = 1/(v+3) + 1/(v-2). Solving for v gives 12 km/h. Then D = 40 km.

AI explanation

Using the formula distance equals the product of speed and time, let the usual speed be s and the usual time be t, so distance D equals s times t. From the given conditions, s times t equals (s plus 3) times (t minus 2/3) and s times t equals (s minus 2) times (t plus 2/3). Expanding both equations and cancelling s times t gives 3t equals 2s/3 plus 3 and 2t/3 equals 2s minus 4/3; solving these yields s equals 12 kmph and t equals 10/3 hours. The distance is 12 multiplied by 10/3, which equals 40 km.

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