Answer
$452.5\text{ rpm}$
Work Step by Step
The diameter of the wheel is $26$ inches so its radius is $\frac{26}{2}=13$ inches.
Linear speed $v=\frac{35\,miles}{h}=\frac{35\times63360\,inches}{60\,min}=36960\text{ inches/min}$
Note that $v$ is also equal to $r\omega$ where $r$ is the radius and $\omega$ is the angular speed.
Thus,
\begin{align*}
r\omega&=13\text{ inches}\times \omega\\
36960\text{ inches/min}&= 13\text{ inches}\times \omega\\
\frac{36960}{13}\text{ rad/min}&=\omega
\end{align*}
With $\frac{1}{2\pi}=1\text{ revolution}$, then
$\omega=\dfrac{36960\text{ rad}}{13\text{ min}}=\dfrac{36960\text{ rad}}{13\text{ min}}\times\dfrac{1\text{ revolution}}{2\pi\text{ rad}}$
$w\approx452.5\,rpm$
