Henry starts a trip when the hands of the clock are together between $8$ a.m. and $9$ a.m.
He arrives at his destination between $2$ p.m. and $3$ p.m. when the hands of the clock are exactly $180^\circ$ apart. The trip takes:
$\textbf{(A)}\ \text{6 hr.}$$\textbf{(B)}\ \text{6 hr. 43-7/11 min.}$$\textbf{(C)}\ \text{5 hr. 16-4/11 min.}$$\textbf{(D)}\ \text{6 hr. 30 min.}$$\textbf{(E)}\ \text{none of these}$