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

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

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

`(1)/(2.5\pi)(rev)/(ft)=(x)/(867)(rev)/(ft)\\\\x=(867)/(2.5*3.14)\\\\x= 110.4\ rev`

therefore

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