Answer
$\frac{\Delta I}{\Delta t}=\frac{V_0}{L}$
$t=\frac{L}{R}=\tau$
Work Step by Step
When $I=0$, $V_R=IR=0$. $V_L=V_0=L\frac{\Delta I}{\Delta t}$
$\frac{\Delta I}{\Delta t}=\frac{V_0}{L}$
$I_{max}=\frac{\Delta I}{\Delta t}t=\frac{V_0}{L}t$
$t=\frac{LI_{max}}{V_0}$
$I_{max}=\frac{V_o}{R}$
$t=\frac{L}{R}=\tau$
