2004 AMC 10B Question 20

In $\triangle ABC$ points $D$ and $E$ lie on $\overline{BC}$ and $\overline{AC},$ respectively. If $\overline{AD}$ and $\overline{BE}$ intersect at $T$ so that $\frac{AT}{DT} = 3$ and $\frac{BT}{ET} = 4,$ what is $\frac{CD}{BD}?$