Answer:
[tex]661.4\ rpm[/tex]
Step-by-step explanation:
we know that
1 mile=63,360 inches
step 1
Find the circumference of the wheels
[tex]C=2\pi r[/tex]
we have
[tex]r=30/2=15\ in[/tex] -----> the radius is half the diameter
substitute
[tex]C=2\pi(15)[/tex]
[tex]C=30\pi\ in[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]C=30(3.14)=94.2\ in[/tex]
Remember that
The circumference of the wheels represent one revolution
Convert 59 miles per hour to inches per minute
[tex]59\ mi/h=59*63,360/60=62,304\ in/min[/tex]
using proportion find the number of revolutions
[tex]\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev[/tex]
therefore
substitute
[tex]62,304\ in/min=661.4\ rev/min=661.4\ rpm[/tex]
