MathDB

Steve has a tricycle which has a front wheel with a radius of

30

cm and back wheels with radii of

10

cm and

9

cm. The axle passing through the centers of the back wheels has a length of

40

cm and is perpendicular to both planes containing the wheels. Since the tricycle is tilted, it goes in a circle as Steve pedals. Steve rides the tricycle until it reaches its original position, so that all of the wheels do not slip or leave the ground. The tires trace out concentric circles on the ground, and the radius of the circle the front wheel traces is the average of the radii of the other two traced circles. Compute the total number of degrees the front wheel rotates. (Express your answer in simplest radical form.)

Problem Statement