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

Answer:

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

Step-by-step 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.

$\begin{array}{rcl}\dfrac{C}{c} & = & \dfrac{2\pi R}{2\pi r}\\\\\dfrac{3c}{c} & = &\dfrac{R}{r}\\\\3 & = & \dfrac{R }{r}\\\\R & = & 3r\\\end{array}$

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