A computerized spin balance machine rotates a $35-$inch$-$diameter tire at $480$ revolutions per minute.

$($a$)$ Find the road speed $($in miles per hour$)$ at which the tire is being balanced. $($Round your answer to two decimal places.$)$

$|$ mph

$($b$)$ At what rate should the spin balance machine be set so that the tire is being tested for $50$ miles per hour? $($Round your answer to two decimal places.$)$ revolutions per minute