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Question
The time for the wheels of a vehicle to make one revolution is reduced by 1/22 of a second when the rate is increased by 15 miles per hour.  Calculate rate of vehicle if the circumferences of the wheels are 6 feet.  Thank you.

Answer
The vehicle travels 6 ft with every revolution of the wheels.

Let t be the seconds it takes for a wheel to make 1 revolution.
Convert 1 revolution/(t seconds) to miles per hour: https://www.flickr.com/photos/dwread/14492308968/
The vehicle is traveling 405/(99t) mph.

When the rate is increased by 15 mph, it takes (t - 1/22) seconds for a wheel to make 1 revolution.
Convert 1 revolution/(t - 1/22 seconds) to miles per hour: https://www.flickr.com/photos/dwread/14492309008/
The faster rate is 405/(99(t - 1/22)) mph.

The difference between these two rates is 15 mph. I'll let you rearrange the equation into quadratic form and solve to get t = 3/22 seconds.
Therefore, the vehicle is traveling 30 mph: https://www.flickr.com/photos/dwread/14492309038/

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Janet Yang

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I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

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I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

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Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

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I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

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George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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