Multiple choice

The wheels of bicycles A and B have radii 30 cm and 40 cm, respectively. While travelling a certain distance, each wheel of A required 5000 more revolutions than each wheel of B. If bicycle B travelled this distance in 45 minutes, then its speed, in km per hour, was

  1. 16 π

  2. 12 π

  3. 18 π

  4. 14 π
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A Correct answer
Explanation

Let distance be D. Revolutions for A = D / (2 * pi * 30), for B = D / (2 * pi * 40). D/(60pi) - D/(80pi) = 5000. D/(240pi) = 5000, D = 1,200,000 * pi cm = 12 * pi km. Speed = Distance / Time = (12 * pi) / (45/60) = 12 * pi / 0.75 = 16 * pi km/hr.

AI explanation

Let the distance be x centimeters; using the circumference formula, the difference in revolutions is x/(2 * pi * 30) - x/(2 * pi * 40) = 5000. Solving this gives x/(60*pi) - x/(80*pi) = 5000, which simplifies to x = 1,200,000*pi centimeters. Converting this to kilometers gives 12*pi kilometers, which bicycle B travels in 45 minutes, or 0.75 hours. The speed is distance divided by time, resulting in 16*pi km/h.

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