Answer:
661.4 rpm
Step-by-step explanation:
we know that
1 mile=63,360 inches
step 1
Find the circumference of the wheels
C=2\pi rC=2πr
we have
r=30/2=15\ inr=30/2=15 in -----> the radius is half the diameter
substitute
C=2\pi(15)C=2π(15)
C=30\pi\ inC=30π in
assume
\pi =3.14π=3.14
C=30(3.14)=94.2\ inC=30(3.14)=94.2 in
Remember that
The circumference of the wheels represent one revolution
Convert 59 miles per hour to inches per minute
59\ mi/h=59*63,360/60=62,304\ in/min59 mi/h=59∗63,360/60=62,304 in/min
using proportion find the number of revolutions
\begin{lgathered}\frac{1}{94.2}\frac{rev}{in}=\frac{x}{62,304}\frac{rev}{in}\\ \\x=62,304/94.2\\ \\x=661.4\ rev\end{lgathered}94.21inrev=62,304xinrevx=62,304/94.2x=661.4 rev
therefore
substitute
62,304\ in/min=661.4\ rev/min=661.4\ rpm62,304 in/min=661.4 rev/min=661.4 rpm
