Buy a level if you don't have one and check the tub. the sides should be level left to right and in to out. Probably isn't, and that is why water is leaking out. Water pooling on the floor, even tile, will leak through (mostly through the grout). ANy cracks make the problem worse. You probably have some cracks in the walls or old leaking caulk at the tile/tub junction. Per the tile council, changes in plane (i.e., corners) and changes in materials (tub to tile) transition should be caulked. Water could be leaking through there, and leaking through the floor, ratherthan that the is outside on the floor visible. If this has been going on for awhile, you could have some structural problems, too. My unprofessional opinion.