Finding distance of traveling pedal when tricycle wheels make one revolution

Question

the front wheel of a child's tricycle has a 10-inch radius and the rear wheels have a 6-inch radius. The pedals are attached to the front wheels by arms that are 7 inches long. How far does a pedal travel when the rear wheels make one revolution?

Answer 1

If the rear wheels make one revolution, the tricycle travels a distance equal to the circumference, C, of the rear wheel.  

 

C = 12π"

 

The front wheel traverses an arc of length 12π" as well.

 

If s is the arc length, then s = rθ, where r is the front wheel's radius

 

So, 12π = 10θ     θ = 6π/5

 

Since the pedals are attached to the front wheel, the angle formed by the initial position of the pedal and the final position of the pedal is also 6π/5

 

So, distance traveled by a pedal = rθ = 7(6π/5) = 42π/5" ≈ 26.39"