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Question
A carriage wheels' circumferences have a 4:5 ratio. The front wheel makes 80 revolutions more than the rear wheel in 1 mile.

Calculate circumference of the wheels.

Mile = 5280 feet

Ratio- 4 + 5 = 9

Circumference- pi * diameter
2 *pi * r

Let F = Front wheel
B = Back wheel

F = B + 80

Not sure how to solve. Thanks.

Answer
The front wheel makes more revolutions, so it is smaller than the rear wheel.

Let c be the circumference in feet of the rear wheel.
The circumference of the front wheel is 4/5 of c = 0.8c

1 mile 5280 ft/mile 1 revolution/(c ft) = (5280/c) revolutions
The rear wheel makes (5280/c) revolutions per mile.

1 mile 5280 ft/mile 1 revolution/(0.8c ft) = (6600/c) revolutions
The front wheel makes (6600/c) revolutions per  mile.

"The front wheel makes 80 revolutions more than the rear wheel in 1 mile."
6600/c = 5280/c + 80
6600/c = 5280/c + 80c/c
6600 = 5280 + 80c
c = 16.5 ft
0.8c = 13.2 ft

Circumferences of the front and rear wheels are 13.2 ft and 16.5 ft, respectively.

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