jmc

The circumference of the front wheel is $2\pi \cdot 2.5=5\pi$ feet. In 100 revolutions, the front wheel travels $5\pi \cdot 100=500\pi$ feet. The back wheel must travel the same distance because they are both attached to the same bike. The circumference of the back wheel is $2\pi \cdot \frac{1}{3}=\frac{2}{3}\pi$ feet (note that 4 inches is equal to $\frac{1}{3}$ feet). Thus, the number of revolutions of the back wheel is $\frac{500\pi }{\frac{2}{3}\pi }=\boxed{750}$.