Answer:
55.94 mph
Step-by-step explanation:
The speedometer is measuring the speed of the vehicle according to the initial configuration.
The number of the revolution, n, that the wheels made in 1 hour is
[tex]n=\frac {\text{Speed}}{\text{Perimeter of the wheel}}[/tex]
Let p and p' be the perimeter of the old and the new wheels respectively.
[tex]P=\pi\times 94.4086[/tex] inches,
[tex]P'=\pi\times 96.0165[/tex] inches.
Since the speedometer is not calibrated according to the new configuration, so, the perimeter of old wheel has been used for the calculation of indicated speed.
[tex]\Rightarrow n=\frac{\text{Speed}}{P}[/tex]
Actually, this number of revolutions in 1 hour is made with the new tires having perimeter P'.
So, the actual speed with new tires is
[tex]=n\times P'[/tex]
[tex]= \frac{\text{Speed}}{P}\times P'[/tex]
[tex]=\frac {55}{\pi\times 94.4086}\pi\times 96.0165[/tex]
[tex]=\frac {55} {94.4086}\times 96.0165[/tex]
[tex]=55.94[/tex] mph
So, the actual speed of traveling is 55.94 mph.
