Understanding Buoyancy: Calculating Mass of a Ship in Different Fluids

[knowNothing23]

53 ••• [SSM] A ship sails from seawater (specific gravity 1.025) into
freshwater, and therefore sinks slightly. When its 600,000-kg load is removed, it
returns to its original level. Assuming that the sides of the ship are vertical at the
water line, find the mass of the ship before it was unloaded.

I'm afraid I have a horrible problem about my conception of volume.

I have solved for the sum of forces in the Y component in both cases. For water and sea water.
My solutions manual shows that one can solve for Vg in water and replace it in the sea water equation. I can't conceive, how this is possible, because a load is taken of the boat when it's in water. Shouldn't the volume change as well? There's more room in the boat.

Thank you.

 

[SteamKing]

The boat rises because it is lighter by 600,000 kg. Remember what Archimedes said about floating objects.

 

[knowNothing23]

True.

Thank you.