d = Diameter of wheels = 25 inches
s = Distance to be traveled by the wheels = 458 miles
Converting the miles to inches
[tex]s=458\times 5280\times 12=29018880\ \text{inches}[/tex]
The distance traveled by the wheels in rotation is the circumference
[tex]D=\pi d\\\Rightarrow D=\pi\times 25[/tex]
The number of rotations required to cover the distance would be
[tex]\dfrac{s}{D}\\ =\dfrac{29018880}{\pi\times 25}\\ =369479.855599[/tex]
[tex]1[/tex] rotation is [tex]360^{\circ}[/tex] so
[tex]369479.855599\times 360=133012748.016^{\circ}[/tex]
The number of rotations to cover the required distance is [tex]133012748.016^{\circ}[/tex]
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