Geometry: Power of a Point & Mass Points · Superchallenge problem

In $\triangle ABC$, $D$ on $AB$ satisfies $AD : DB = 1 : 2$ and $E$ on $AC$ satisfies $AE : EC = 1 : 2$. Segments $BE$ and $CD$ meet at $P$. What fraction of the area of $\triangle ABC$ is the area of $\triangle BPC$?