Question

on a vehicle , the front tire makes 3 revolutions for everyone revolution the back tire makes. how many times larger is the radius of the back tire than the radius of the front tire?

Answer 1

`\boxed{\text{Two times larger}}`

Explanation:

Let the radius and circumference of the back tire be R and C, respectively. Then

C = 2πR

Similarly, for the front tire,

c = 2πr

The front tire makes three revolutions for every one the back tire makes, so

3c = C

Compare the two tires.

`\begin{array}{rcl}(C)/(c) & = & (2\pi R)/(2\pi r)\\\\(3c)/(c) & = &(R)/(r)\\\\3 & = & (R )/(r)\\\\R & = & 3r\\\end{array}`

`\text{The radius of the back tire is $\boxed{\textbf{two times larger than}}$}\\\text{ or \textbf{three times as large as} the radius of the front tire}`