$(13\mathrm{.}1\mathrm{.}20)$ One time, as I was driving south on Inglewood Ave on an early Sunday morning, an idiotface jerk passed me traveling in the same direction. I recognized the change in pitch as a

minor third, or approximately a $\backslash (16\backslash \%\backslash )$ drop in the frequency. $($Hum to yourself the first two notes in the "Star Spangled Banner." That's what it sounded like.$)$

$($a$)$ Assuming that I was not moving, how fast was this jerkhead traveling? Give your answer in units of $\backslash (\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$hr$\}\backslash ).$

$($b$)($Optional$)$ Assuming that my speed was $\backslash (20\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$hr$\}\backslash ),$ how fast was this jerkhead traveling? $($The answers to parts $($a$)$ and $($b$)$ will not be that different.$)$

Take the speed of sound to be $\backslash (340\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).($It was a somewhat cool morning, which lowers the speed of sound.$)$