Multiple choice

A robotic vehicle was assigned to cover a fixed distance on a test track at a constant speed. If its speed had been increased by 3 km/hr, it would have completed the journey 3 hours sooner. On the other hand, if its speed had been reduced by 2 km/hr, it would have taken 7 hours longer. What was the distance, in kilometers, that the robot travelled?

  1. 32

  2. 24

  3. 28

  4. 18
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance be D and speed be v. D/v - D/(v+3) = 3 and D/(v-2) - D/v = 7. Solving these equations: D = 3v(v+3)/3 = v(v+3) and D = 7v(v-2)/2. Equating them: 2v(v+3) = 7v(v-2) -> 2v+6 = 7v-14 -> 5v = 20 -> v = 4. D = 4(4+3) = 28.

AI explanation

Let the distance be D, the original speed be S, and the original time be T; we establish the equations D = S * T, D = (S + 3) * (T - 3), and D = (S - 2) * (T + 7). Equating the first two gives 3T - S = 3, and equating the first and third gives 2T - S = -7. Solving this system yields T = 4 hours and S = 9 km/hr, making the distance 28 kilometers.

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