1970 AHSME Problem 29

It is now between 10:00 and 11:00 o'clock, and six minutes form now, the minute hand of the watch will be exactly opposite the place where the hour hand was three minutes ago. What is the exact time now?

\begin{array}{l} \textbf{(A) }10:05\dfrac{5}{11}\qquad \textbf{(B) }10:07\dfrac{1}{2}\qquad \textbf{(C) }10:10\qquad\\ \textbf{(D) }10:15\qquad \textbf{(E) }10:17\dfrac{1}{2} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.