Question

Bicycles in the late 1800s looked very different than they do today. How many rotations does each tire make after traveling 600 feet? Round your answers to the nearest whole number.

Answer 1

Step 1: Calculate the circumference of larger and smaller tire.

Given:

Diameter of the larger tire (${\mathrm{d}}_1$) = $60$ inches

Radius of the smaller tire ($r_2$) = $9$ inches

Total distance traveled by the tires = $600$ feet

We know that,

Circumference of larger tire ($C_1$):

$\Rightarrow$$C_1$= ${\mathrm{\pi d}}_1$

$\Rightarrow$$C_1$= $3.14\times 60$ [$\because \mathrm{\pi }=3.14$]

$\Rightarrow$$C_1$= $188.4$inches

$\Rightarrow$$C_1$=$\frac{188.4}{12}$feet [$\because 1feet=12inches$]

$\therefore$ $C_1$=$15.7$feet

And Circumference of smaller tire ($C_2$):

$\Rightarrow$$C_2$= $2\pi r_2$

$\Rightarrow$$C_2$= $2\times 3.14\times 9$ [$\because \mathrm{\pi }=3.14$]

$\Rightarrow$$C_2$= $56.52$inches

$\Rightarrow$$C_2$=$\frac{56.52}{12}$feet [$\because 1feet=12inches$]

$\therefore$ $C_2$= $4.71$feet

Step 2: Find the number of revolutions by both the tires.

We also know that,

Number of revolutions =$\frac{Totaldis\tan cetravelled}{Circumferenceoftire}$

For larger tire:

$\Rightarrow$ Number of revolutions = $\frac{600}{15.7}$

$\Rightarrow$ Number of revolutions = $38.21$

$\therefore$ Number of revolutions = $38$

For smaller tire:

$\Rightarrow$ Number of revolutions = $\frac{600}{4.71}$

$\Rightarrow$ Number of revolutions = $127.38$

$\therefore$ Number of revolutions = $127$

Hence, After traveling 600 feet, larger tire will make $38$ revolutions and smaller tire will make $127$ revolutions.