How Do You Design a Chain and Sprocket System for a 25mph Scooter?

[gongsta]

Homework Statement

You would like to build a little scooter using an engine. The rear drive wheel/tire that you have is 16 inches in total diameter. You also have a 16 tooth sprocket gear (approx. 2.5 inches in diameter) that will fit on the engine crankshaft. Design a chain and sproeckt system that will allow your scooter to travel at 25mph at rated engine speed.
engine horsepower: 5
engine speed: 3600rpm
note: there must be an intermediate gear and sprocket between the engine(and sprocket) and the back tire, also my professor confirmed that the sprocket on the back tire does not have 109 teeth.

Homework Equations

The Attempt at a Solution

back tire speed: 525 rpm
engine speed: 26.77 mph
I can seem to find no matter what equation I use to find any details about the middle sprocket.

 

[darkys]

I don't know what equation to use to solve this or if I am missing something. Can anyone help me out?