Jupiter is about $900$ million kilometers from Earth. A probe is traveling through space towards Jupiter and periodically emits a $1$ GHz radio pulse while listening for the return echo. The time to the echo tells the probe how soon it will crash into Jupiter.

a$)$ Right after leaving Earth, how long will it take to receive an echo from Jupiter?

b$)$ The probe is slowing down but still going $1$ km$/$s and receives an echo after $66\mathrm{.}6$s$.$ How soon until it hits Jupiter?