Question

A tire with a diameter of 30 inches is on a vehicle being driven 867 ft/min. to the nearest unit, how many revolutions per minute are made by the tire?​

Answer 1

Answer:

The number of revolutions per minute that are made by the tire is 110

Step-by-step explanation:

step 1

Find the circumference of the tire

The circumference of a circle is

$C=2\pi r$

we have

1 ft=12 in

Convert in to ft

$D=30\ in$

$D=30\ in=30/12=2.5\ ft$

$r=2.5/2=1.25\ ft$ ----> the radius is half the diameter

substitute

$C=2\pi(1.25)$

$C=2.5\pi\ ft$

Remember that one revolution represent the length of the circumference

so

using proportion

Find out how many revolutions are made by the tire in one minute

Let

x -----> the number of revolutions in one minute

$\frac{1}{2.5\pi}\frac{rev}{ft}=\frac{x}{867}\frac{rev}{ft}\\\\x=\frac{867}{2.5*3.14}\\\\x= 110.4\ rev$

therefore

The number of revolutions per minute that are made by the tire is 110