2005 Cayley Problem 23

At 12:00 noon, Anna and Bill left home and walked in the same direction. Anna walked at 4 km/h and Bill walked at 3 km/h. At 12:15 their dog Dexter, running at 6 km/h, left home to run after them. The dog ran until it caught up to Anna, then it ran back to Bill. (In his excitement, Dexter lost no time in turning around once he reached Anna.) At what time did Bill meet Dexter on Dexter's way back?

\textbf{(A)}\ 1:00 p.m.\quad \textbf{(B)}\ 1:15 p.m.\quad \textbf{(C)}\ 12:45 p.m.\quad \textbf{(D)}\ 1:05 p.m.\quad \textbf{(E)}\ 12:50 p.m.

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.