Weird Ratio

In $\triangle{ABC}$ , Let $D$ and $E$ be the trisection points of $BC$ with $D$ between $B$ and $E$ . Let $F$ be the midpoint of $AC$ , and let $G$ be the midpoint of $AB$ . Let $H$ be the intersection of $EG$ and $DF$ . If the ratio $EH:HG$ equals $a:b$ where $a,b$ are relatively prime positive integers. Find $a+b$ .