Why does Alka Seltzer dissolve faster in Apple juice than in water?

Baking soda (and all soluble solids) disolve faster in hot water because the heat makes the water molecules move faster. Therefore, they can break up the baking soda into individual ions faster: when a sodium or hydrogen atom is an the edge of a clump of baking soda, the oxygens of water molecules surround them and pull them off. That exposes a carbonate ion, which the hydrogens of water molecules surround and pull off. This repeats until all of the baking soda is broken down into ions.