Question

The factory tires for your vehicle are P220/55R17 with circumference of 94.4086 inches. You have decided to purchase some used P265/65R17 with circumference of 96.0165

inches and have a friend install them for you. Since the calibration was not changed in your vehicle, when the speedometer reads 55 mph, how fast will you actually be
traveling?

Answer 1

55.94 mph

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

`n=\frac {\text{Speed}}{\text{Perimeter of the wheel}}`

Let p and p' be the perimeter of the old and the new wheels respectively.

`P=\pi* 94.4086` inches,

`P'=\pi* 96.0165` 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.

`\Rightarrow n=\frac{\text{Speed}}{P}`

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

`=n* P'`

`= \frac{\text{Speed}}{P}* P'`

`=\frac {55}{\pi* 94.4086}\pi* 96.0165`

`=\frac {55} {94.4086}* 96.0165`

`=55.94` mph

So, the actual speed of traveling is 55.94 mph.