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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.

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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