The activity $A$ after $n$ half-lives is given by $A = A_0 (\frac{1}{2})^n$. Given $\frac{A}{A_0} = \frac{1}{16} = (\frac{1}{2})^4$, so $n = 4$. Total time $t = n \times T_{1/2} = 4 \times 20 = 80$ minutes.