An expert cyclist can attain a speed of 40mi/hr if the sprocket assembly has r

_{1}=5in, r

_{2}=2in, and the wheel is 28in in diameter.

Approximately how many revolutions per minute of the front sprocket wheel will produce a speed of 40mi/hr?

*(Hint: First change 40mi/hr into in/sec)*

Clarifications:

The front sprocket is referring to the larger sprocket (5in)(it has the pedals on it). The smaller sprocket (2in) is attached to the wheel (28in diameter). This is all shown in a diagram in the book that you, unfortunately cannot see.

My post:

I've worked this problem a number of different ways, and have proved that s/t=r(theta)/t, but I haven't come up with much else.

The answer in the back of my book is telling me 192.08 revolutions/minutes. I have yet to connect the two through a mathematical equation.

I'm mostly just frustrated by it.