If this is the same toilet as the one with the leak to the floor, are you sure the water handle is turned open all the way? If it's slow to fill, then either the faucet isn't all the way on, or the fill valve (big thing on the left in your tank) is shot and needs to be replaced), or the toilet is leaking so fast into the bowl that the tank can't fill fast. (It could also be a kinked line, but I don't see those in the picture in your other thread.)