In rectangle A B C D, A B=6 and B C=3. Point E between B and C, and point F between E and C are such that B E=E F=F C. Segments \overline{A E} and \overline{A F} intersect \overline{B D} at P and Q, respectively. The ratio B P: P Q: Q D can be written as r: s: t, where the greatest common factor of r, s, and t is 1 . What is r+s+t ?
Answer Choices
A. 7
B. 9
C. 12
D. 15
E. 20