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The odometer (mileage gauge) of a car tells you the number of miles you have driven, but it doesn't count the miles directly. Instead, it counts the number of revolutions of your car's wheels and converts this quantity to mileage, assuming a standard size tire and that your tires do not slip on the pavement.

- A typical midsize car has tires 24.0 inches in diameter. How many revolutions of the wheels must the odometer count in order to show a mileage of 0.100 mile?

- What will the odometer read when the tires have made 5800 revolutions?

- Suppose you put oversize 32.0 inch-diameter tires on your car. How many miles will you really have driven when your odometer reads 350 miles?

Answer :

Answer:

[tex]n=84.03381\,revolutions[/tex]

[tex]s=6.9\,miles[/tex]

Explanation:

-

Given that:

Diameter of the tyre, [tex]d=24\,in[/tex]

distance covered, [tex]s=0.1\,mile[/tex]

Now we find the circumference of the tyre:

[tex]P=\pi.d[/tex]

[tex]P=\pi\times 24[/tex]

[tex]P=75.3982\,inches[/tex]

Since

[tex]s=0.1\times 63360=6336\,inches[/tex]

No. of revolutions for the given distance,

[tex]n=\frac{s}{P}[/tex]

[tex]n=\frac{6336}{24\pi}[/tex]

[tex]n=84.03381\,revolutions[/tex]

-

Given that:

No. of revolutions, [tex]n=5800[/tex]

Now, as we have distance covered in one revolution will be equal to the circumference of the tyre.

So,

The odometer reading will be:

[tex]s=P\times n[/tex]

[tex]s=\frac{24\pi}{63360} \times 5800[/tex]

[tex]s\approx 6.9\,miles[/tex]

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