The treadmill at Robert's gym is run by a belt and wheel system.

A motor spins wheel A which is attached by a belt to wheel B.

Wheel B is fixed by an axle to wheel C which spins the conveyor that Robert runs on.

The machine is set to run the conveyor at a pace of 1 mile every 8 minutes.

The figure is not to scale.

The radius of wheel A is 0.9 inches, the radius of wheel B is 0.75 inches, and the radius of wheel C is 3 inches.

At what angular speed is the motor rotating wheel A? Give your final answer in revolutios per minute.

This is what I know:

The equations:

s=rΘ

Θ=wt

v=wr (This is the one I will use)

1) I know that it's a pace of 1 mile every 8 minutes, so 1/8 = 0.125

2) Thus, v_{C}=^{0.125mi}/_{min}, now find w_{A }3) v_{C}=w_{C}r_{C}->^{0.125mi}/_{min}=w_{c}(3)

4)^{7920in}/_{min}(converted miles to inches)

5) w_{C}=2640(^{1rev}/_{2pi})-420.169 = w_{B }

Though I'm not really sure where the -420.169 came from, I had my teacher help me but I didn't quite understand, can someone explain it to me and what I should do next after this?

Thanks!

Answer is supposed to be 350.1409 rpm (from what my teacher said)