You are here:

Advanced Math/Circumference


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.

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.

Advanced Math

All Answers

Answers by Expert:

Ask Experts


Janet Yang


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.


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

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

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

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

©2016 All rights reserved.