We present an improved determination of the total width of the top quark, ${\ensuremath{\Gamma}}_{t}$, using $5.4\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity collected by the D0 Collaboration at the Tevatron $p\overline{p}$ Collider. The total width ${\ensuremath{\Gamma}}_{t}$ is extracted from the partial decay width $\ensuremath{\Gamma}(t\ensuremath{\rightarrow}Wb)$ and the branching fraction $\mathcal{B}(t\ensuremath{\rightarrow}Wb)$. $\ensuremath{\Gamma}(t\ensuremath{\rightarrow}Wb)$ is obtained from the $t$-channel single top-quark production cross section and $\mathcal{B}(t\ensuremath{\rightarrow}Wb)$ is measured in $t\overline{t}$ events. For a top mass of 172.5 GeV, the resulting width is ${\ensuremath{\Gamma}}_{t}={2.00}_{\ensuremath{-}0.43}^{+0.47}\text{ }\text{ }\mathrm{GeV}$. This translates to a top-quark lifetime of ${\ensuremath{\tau}}_{t}=({3.29}_{\ensuremath{-}0.63}^{+0.90})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}25}\text{ }\text{ }\mathrm{s}$. We also extract an improved direct limit on the Cabibbo-Kobayashi-Maskawa quark-mixing matrix element $0.81<|{V}_{tb}|\ensuremath{\le}1$ at 95% C.L. and a limit of $|{V}_{t{b}^{\ensuremath{'}}}|<0.59$ for a high-mass fourth-generation bottom quark assuming unitarity of the fourth-generation quark-mixing matrix.