fill the bath with a little water.take bath panel off and inspect the trap as to where its leaking from when you pull the plug.most likely leaking from the trap or where it joins the waste pipe.as for the slow empty time this is due to a blocked trap or incorrect waste pipe diameter 1inch and a half for baths and 1 inch and a quarter for basins.
ozone, December 2011
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How to fix problem of water coming from under Bath tub?