The circumference of a rear wheel of a carriage is 50 inches more than a front wheel. If the rear wheel makes as many revolutions in going 200 feet as the front wheel in going 120 feet, find the length of the circumference of each wheel.

Answer 1

Radius of large wheel --- R
radius of smaller wheel -- r

Circumf of large = 2πR
circumf of small = 2πr
2πR - 2πr = 50
R - r = 25/π
R = 25/π + r

rotations of front wheel = 1440/(2πr) = 720/(πr)
rotations of rear wheel = 2400/(2πR) = 1200/(πR)

but 1200/πR = 720/πr
1200πr = 720πR
5r = 3R
3(25/π + r) =5r
75/π + 3r = 5r

r = 75/2π = appr 11.9366
R = appr 19.8944

carry on