Question

how many revolutions will the tire have made after traveling one mile?

Answer 1

Step 1: Let's find the circumference of the tire in feet.

Given:

Recall: 1 foot = 12 inches

Radius = 13 inches = 13 ÷ 12 = 13/12 Feet

We get,

$\text{ Circumference = 2}\pi r$$\text{ = 2}\pi(\frac{13}{12})$$\text{ Circumference = }\frac{26}{12}\pi\text{ = }\frac{13}{6}_{}\pi\text{ feet}$

Step 2: Let's now determine the number of revolutions that tire will have in 1 mile.

$\text{ Total number of revolutions = }\frac{\text{ 1 mile}}{\text{ Circumference of the tire}}$

Recall: 1 mile = 5280 feet

We get,

$\text{ Total number of revolutions = }\frac{\text{ 5}280}{\frac{13\pi}{6}_{}}$$\text{ = 5280 x }\frac{\text{ 6}}{13\pi}$$\text{ = }\frac{\text{ 3}1680}{13\pi}$$\text{= }\frac{\text{ 3}1680}{13\pi}\text{ = }\frac{31680}{13(3.1416)}\text{ = 775.69489334195}$$\text{ Total number of revolutions }\approx775.69\text{ }$

Therefore, the answer is 775.69 revolutions.