Silver based prints can last for well over 100 years or so but this can depend on many variables.
Firstly the reason they do last is because Silver is an extremely stable element and being a noble metal means it does not react or corrode in air or with many ( if any ) chemicals that occur in nature.
The longevity of silver based prints is also affected by the paper used and when a print fades or discoulors it is mostly due to the paper, how you process the print can also have a large impact of print life and the main cause of prints prematurely aging is due to poor washing and not removing all of the fixer after developing, this is even more critical for fiber base papers than resin coated papers as with FB papers the fixer really gets into the paper and this takes time to thoroughly wash out, if do not wash all the fixer out this will over a short time eat away at the paper and generally looks like crap like some one peed on it, not a nice look at any time, another thing to take into account is that prints to be be fully fixed so that only metallic silver remains and all silver halide is removed, an under fixed print may have very unpredictable and undesirable results when toning as well.
Resin Coated ( RC ) papers are much easier to handle than FB papers because it is as the name says coated in a resin and therefore sealing the paper making it harder for the fixer to get into the grain of the paper, even my self when I am using RC papers I do not get to fussy with washing and around 5 mins is fine where as when I use FB papers I will wash for over 10 mins in a constant fresh water supply.
Toning can extend the life of a print by decades, chemical toning is done by converting the silver to more stable elements and these element in most cases have different colours than that of pure silver so giving a tone to the print, common toning is sepia, selenium and gold, sepia toning converts the silver to silver sulfide witch has a brown like colour and is even more stable than pure silver meaning the print will last longer, selenium and gold toning do a similar thing although they are both also commonly used with out making much or any difference to the print tone. I my self use sepia tone only for when I want that look and if I do not I use selenium or gold that can be done with very little change in the print, for maximum print life I believe gold toning to be the best but it is also bloody expensive.
RC Vs FB , and age old question for many of us and to tell the truth I have no idea what would last the longest, instinct tells me that FB paper is the best for long life but I have no way of either proving or disproving this, I have 30 to 40 year old prints done with both that still look as good as the day they where printed. There are plenty of FB prints well over 100 years old but in fairness to RC papers have not been around this long so of course there will be no examples.
How a print is stored or displayed will have a huge impact on its life, in a smoky house nicotine will stain prints and eat away at the paper reducing its life considerably, there could also be other chemically induced contaminates from cooking and cleaning and general atmospheric pollution that will reduce a print life and of course the biggest killer of any print is the sun, no print will last very long if it is in sunlight.
Taking all of this into account means a print can last anywhere from a few weeks to over 100 years
Sorry I could not be a bit more precise