Question

the circumference of the rear wheel of a unusual bicycle is 3 feet more than the circumference of the front wheel. The rear wheel makes 100 fewer rotations than the front wheel in traveling 6000 feet. Find the circumference of the rear wheel

Answer 1

C = 2 r π
n - number of rotations of the front wheel
n *2 r π = 6000
( n - 100 ) 2 ( r + 3 ) π = 6000
n r π = ( n - 100 ) ( r +3 ) π
n r π = n r π + 3 n π - 100 r π - 300 π / : π
3 n = 100 r + 300
2 (100 r + 300 )/3 * r π = 6000
r π ( 100 r + 300 ) = 9000
100 r² π + 300 r π - 9000 = 0 /: 100
π r² + 3 π r - 90 = 0
r = - 3π +/- √(9π² + 360π) / 2 π ≈ 4 ft
The rear wheel:
r + 3 = 7 ft ( unusual bicycle )
C = 2 r π = 2 * 7 π = 14 π ft