Answer:
Step-by-step explanation:
Let the speedometer reading is [tex]S_0=63[/tex] mph, perimeter of factory-installed tires is [tex]P_0=75.1[/tex] inches and perimeter of current tires is [tex]P=82.4[/tex] inches.
The speedometer reading, [tex]S_0[/tex], is based on the number of actual revolution of tires in [tex]1[/tex] second, [tex]n[/tex], and on the perimeter of installed tires, [tex]P_0[/tex] , as
[tex]S_0=n\times P_0 \Rightarrow n=\frac{S_0}{P_0}\;\cdots (i)[/tex]
Let [tex]S[/tex] be the actual speed of SUV having actual perimeter [tex]P=82.4[/tex] inches,
[tex]\Rightarrow S=n\times P[/tex]
[tex]\Rightarrow S= \frac{S_0}{P_0}\times P[/tex] [from equation [tex](i)[/tex]]
So, from the given values, we have
[tex]S= \frac{63}{75.1}\times 82.4[/tex] mph
[tex]\Rightarrow 69.124[/tex] mph
Hence, the actual speed of the SUV is [tex]69.124[/tex] mph.
