Buoyant Force and Archimedes Principle

(Problem from F = ma 2016) A container holds a layer of oil sitting on top of a layer of water. A wooden block can be placed in equilibrium in this container such that $\frac{1}{3}$ of the block lies above the oil, $\frac{1}{3}$ of the block is submerged in the oil, and $\frac{1}{3}$ of the block is submerged in the water.

Now, the block is placed in a new container which has only oil. At equilibrium, what fraction of the block is submerged in the oil? It is known that the respective densities of oil and water are $\rho_o = 800 \frac{\text{kg}}{\text{m}^3}$ and $\rho_w = 1000 \frac{\text{kg}}{\text{m}^3}.$