Answer
$\approx 346$ miles
Work Step by Step
The difference in latitudes gives the central angle of
$\theta=35^{o}-30^{o}=5^{o}$
To convert into radians, multiply by $\pi/180^{o}$.
$\displaystyle \theta=\frac{5^{o}\pi}{180^{o}}=\frac{\pi}{36}$ rad
The length $s$ of an arc that subtends
a central angle of $\theta$ radians is $ s=r\theta$.
$ s=\displaystyle \frac{\pi}{36}\cdot 3960\approx$345.575191895
$\approx 346$ miles
