2002 AMC 10A Problem 20

Points $A,$ $B,$ $C,$ $D,$ $E,$ and $F$ lie, in that order, on $\overline{AF},$ dividing it into five segments, each of length $1.$ Point $G$ is not on line $AF.$ Point $H$ lies on $\overline{GD},$ and point $J$ lies on $\overline{GF}.$ The line segments $\overline{HC},$ $\overline{JE},$ and $\overline{AG}$ are parallel. Find $\frac{HC}{JE}.$