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QUESTION: The front wheel of a carriage makes 6 revolutions more than the rear wheel in traveling 360 feet. If the circumference of each wheel was 3 feet larger, the front wheel would make 4 revolutions more than the rear wheel in traveling the same distance. Determine circumference of each wheel.

ANSWER: Let f and r be the circumferences in feet of the front and rear wheels, respectively.
Number of revolutions = (distance traveled)(circumference of wheel)

"The front wheel of a carriage makes 6 revolutions more than the rear wheel in traveling 360 feet."
Express r in terms of f:
https://www.flickr.com/photos/dwread/15252429598/

"If the circumference of each wheel was 3 feet larger, the front wheel would make 4 revolutions more than the rear wheel in traveling the same distance."
Express r in terms of f:
https://www.flickr.com/photos/dwread/15252429628/

Solve for f:
https://www.flickr.com/photos/dwread/15416003716/

The circumference of the front wheel is 12 ft.
The circumference of the rear wheel is 15 ft.


---------- FOLLOW-UP ----------

QUESTION: I don't understand your calculations for the following:

first part of solution- third line (r=).

second part of solution- all after first line.

Thanks again.

Answer
In order to express r in terms of f, r has to be moved out of the denominator and given a coefficient of 1:
https://www.flickr.com/photos/dwread/15254636107/

After being increased by 3 ft, the circumferences of the front and rear wheels are f+3 and r+3, respectively.
The front wheel makes 360/(f+3) revolutions and the rear wheel makes 360/(r+3) revolutions.
This time, you need to move r+3 out of the denominator:
https://www.flickr.com/photos/dwread/15254954938/  

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