I used to sell Asbestos, siding, flooring, flat sheets, corrugated sections and blown on insulation. There was and is not today a better product for what it was designed and intended for. HOWEVER, it is a dangerous product during manufacture, installation and removal. As stated by Guitarman the "gestation" period is anywhere from 20 years on, depending on ones immune system abilities. We sold both 9" and 12" asbestos tiles.
Two recommendations, if you are concerned I would contact a federally licensed abatement company to come in and test the tile and if it's asbestos have them remove it. If it has not been disturbed you might, if you have the clearances, consider a new sub floor on top of the tile 1/4" thick and lay that down on top prior to installation of any new final surface. Some folks might recommend wetting the floor and remove it yourself, I would not. I've sat thru enough trials and testified enough to come to an understanding with myself that when it comes to asbestos I don't f around.
tamvalleyman: if you had NO tile my guess is you did not remove any asbestos. We never sold flooring rolls or subfloors - except some people used our flat sheets as a subfloor in bathrooms, but I doubt it would have been used in a travel trailer in large sheets as it was pretty brittle and the flexing would have cracked the sheets.
Armstrong, not the company I worked for, also used a lot of asbestos in their flooring and their ceiling tiles when it was perfectly legal as did a lot of insulation companies.
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