Uniform wire $W_1$ with $1\mathrm{.}0$ m in length and $1\mathrm{.}0$ mm in diameter is connected to one end of another uniform wire $W_2$ of the same material with $2\mathrm{.}0$ m in length and $2\mathrm{.}0$ mm in diameter. A voltage source is connected across the wires and a current is passed through them. If it takes an average time of $s$ for a conduction electron to travel through wire $W_1,$ how long does it take for such an electron to travel through wire $W_2?$