Buoancy (block floating in water)

[etagg]

Im confused by this question:

A block of wood floats above water with 90% of its volume submerged. Oil with a density of 875kg/m^3 is then poured over the block so that it covers the entire block. Find the fraction of the block now submerged in water.

I know that the fraction of the block submerged will decrease.
I started by recognizing that the initial force of buoyancy is equal to the final force of buoyancy

ρ_w g(0.9)V=ρ_w gxV+ρ_o g(1-x)V

Where the V and g cancel out, and the x is equal to the portion of the volume submerged in the water and the oil.
However, when i use this method, x equals 0.9, meaning that the same amount of the block is submerged in the water, when it should be less of the block is submerged in the water.
Please help!

 

[Doc Al]

I started by recognizing that the initial force of buoyancy is equal to the final force of buoyancy

ρ_w g(0.9)V=ρ_w gxV+ρ_o g(1-x)V

OK.

Where the V and g cancel out, and the x is equal to the portion of the volume submerged in the water and the oil.

x is the fraction of the block submerged in water.

However, when i use this method, x equals 0.9, meaning that the same amount of the block is submerged in the water, when it should be less of the block is submerged in the water.

Please show how you solved for x.

 

[etagg]

ohhhh, what a stupid mistake. I mistakenly factored 0.9 when i should not have. Goes to show what happens when you look at a problem for too long!
thanks for your help.