Here is a problem that I am stuck on: On an old-fashioned bicycle the front wheel has a radius of $2.5$ feet and the back wheel has a radius of $4$ inches. If there is no slippage, how many revolutions will the back wheel make while the front wheel makes $100$ revolutions?
So, the front wheel has circumference 2*2.5* $\pi$ = 5 $\pi$. That means it moves 5*100 = 500 $\pi$ after 100 revolutions.
Then we divide this by 2*4 = 8 $\pi$ which is equal to 62.5. So the back wheel moves this many revolutions? Why am I wrong?