Math CentralQuandaries & Queries


Question from Joi, a student:

To approximate the speed of the current of a river, a circular paddle wheel with radius 4 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 10 revolutions per minute, what is the speed of the current? Express your answer in miles per hour.

Hi Joi,

The paddle wheel in the river functions like a wheel rolling on a road. The radius of the paddle wheel is 4 feet so its circumference is 2 π r = 2 × π × 4 = 251.33 feet. Since the wheel makes 10 revolutions per minute a point on the circumference of the paddle wheel travels 10 × 251.33 = 2513.3 feet each minute. Hence the river is flowing at 2513.3 feet per minute which is 2513.3/5280 = 0.48 miles per hour.


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