Question

Your speedometer reading is 63 mph, but your tires are larger than the original factory-installed tires. How fast is your SUV actually moving? The circumference of the factory-installed tires was 75.1 inches, but your current tires are 82.4 inches around.

Answer 1

Explanation:

Let the speedometer reading is
`S_0=63` mph, perimeter of factory-installed tires is
`P_0=75.1` inches and perimeter of current tires is
`P=82.4` inches.

The speedometer reading,
`S_0`, is based on the number of actual revolution of tires in
`1` second,
`n`, and on the perimeter of installed tires,
`P_0` , as

`S_0=n* P_0 \Rightarrow n=(S_0)/(P_0)\;\cdots (i)`

Let
`S` be the actual speed of SUV having actual perimeter
`P=82.4` inches,

`\Rightarrow S=n* P`

`\Rightarrow S= (S_0)/(P_0)* P` [from equation
`(i)`]

So, from the given values, we have

`S= (63)/(75.1)* 82.4` mph

`\Rightarrow 69.124` mph

Hence, the actual speed of the SUV is
`69.124` mph.