A $300-$km$-$long high$-$voltage transmission line $2\mathrm{.}0$ cm in diameter carries a steady current of $1,170$ A$.$ If the conductor is copper with a free charge density of $8\mathrm{.}51028$ electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? $($Use $3\mathrm{.}156107$ for the number of seconds in a year.$)$