Multiple choice

In a motorcycle race, one of the three motorbikes that started out at the same time was at 15 kmph less than the first one and 3 kmph more than the third one. It arrived at the terminal point 12 minutes after the first motorbike and 6 minutes before the third one. There were no stops en route. What is the time taken by the third motorbike?

  1. 30 min

  2. 1 h

  3. 1 h 12 min

  4. 1 h 15 min
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A Correct answer
Explanation

Let the speeds be v1, v2, v3. We have v2 = v1 - 15 and v2 = v3 + 3. Using time = distance/speed and the time differences (12 min = 0.2 h, 6 min = 0.1 h), we set up equations for the distance D: D/v2 - D/v1 = 0.2 and D/v3 - D/v2 = 0.1. Solving these yields the time taken by the third motorbike.

AI explanation

Let the three motorbikes be A, B, and C; based on the problem, the speed differences are A - B = 15 and B - C = 3, making A - C = 18. Letting the speeds be x+18, x+3, and x, the distance is constant, so using the distance formula we equate the distances: (x+18)(t) = (x+3)(t+12) = x(t+18). Expanding the middle and right side equality gives xt + 18t + 3t + 36 = xt + 18x, and expanding the left and middle equality gives xt + 18t = xt + 12x + 3t + 36. Solving these equations reveals that x equals 36 and the time t for the first motorbike is 0.5 hours. Adding the 12 minutes (0.2 hours) it arrived after the first, the time taken by the third motorbike is 30 min. The time taken by the third motorbike is 30 min.

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