SOLUTION: The circumference of a rear wheel of a certain wagon is 3 feet longer than the circumference of the front wheel. The rear wheel makes 100 fewer revolutions than the front wheel in
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Question 349235: The circumference of a rear wheel of a certain wagon is 3 feet longer than the circumference of the front wheel. The rear wheel makes 100 fewer revolutions than the front wheel in travelling a distance of 6000 feet. Find the circumference of each wheel. Answer by solver91311(24713) (Show Source):
Let represent the circumference of the smaller wheel. Then is the circumference of the larger wheel. Divide the circumference into the distance traveled to get the number of revolutions. Let be the number of revolutions of the front wheel. Then the number of revolutions of the back wheel must be
Now we can write two equations:
and
Solve the second equation for :
Verification of the addition in the last step is left as an exercise for the student.
Now that we have two different expressions both equal to , set them equal to each other:
Cross-multiply, collect like terms, and put the equation into standard form:
Divide both sides by 100:
Factor, solve the quadratic, discard the negative root. The positive root will be the circumference of the smaller wheel. The positive root plus three will be the circumference of the larger wheel.
John
My calculator said it, I believe it, that settles it
