Question 19
In rectangle $ABCD,$ $AB=6$ and $BC=3.$ Point $E$ between $B$ and $C,$ and point $F$ between $E$ and $C$ are such that $BE=EF=FC.$ Segments $\overline{AE}$ and $\overline{AF}$ intersect $\overline{BD}$ at $P$ and $Q,$ respectively.
The ratio $BP:PQ:QD$ can be written as $r:s:t$ where the greatest common factor of $r,$ $s,$ and $t$ is $1.$ What is $r+s+t?$
The ratio $BP:PQ:QD$ can be written as $r:s:t$ where the greatest common factor of $r,$ $s,$ and $t$ is $1.$ What is $r+s+t?$