Problem $3(4$ points$)$: A planetary system with sun, ring, planet, and carrier, consists of a ring gear of $160$ teeth, and a planet of $40$ teeth. The sun and ring gears act as inputs. Angular velocity of sun is $250$ rpm CCW$,$ and that of the ring is $300$ rpm CW $.$

a$)$ What is the output member of the system? Determine the number of teeth on the sun gear

b$)$ Let the sun and ring gears be the inputs. Showing all steps and utilizing the tabular form, $($show all steps and your own table for full credit$),$ obtain the angular velocity of the carrier

c$)$ Using the tables you constructed for part $($b$),$ what is angular velocity of the planet?