Zoom International Math League

First to clarify the problem, it should be $AD:DC=1:2$, right?

There are many different solutions here, but most rely on using the ratio of areas for triangles when they share a base or share a height.

For example, let $[ABC]$ denote the area of $\mathrm{△}ABC$ so $[ABC]=360$. Since $AD:AC=1:2$ triangles $\mathrm{△}ABD$ (with base $AD$) and $\mathrm{△}CBD$ (with base $CD$) share a height, so their ratio of areas$$[ABD]:[CBD]=1:2.$$Since the areas add up to $360$, we have $[ABD]=120$ and $[CBD]=240$.

Using this type of reasoning is key to the problem. One nice way to proceed is to let $G$ be on $BC$ so that $\overline{EG}$ is parallel to $\overline{AC}$. What similar triangles can you find from here?