With average drive parts, 3000 miles seems to be a fairly common range for chain life on a derailleur geared bicycle while a good cassette will last through 2 and perhaps 3 chains.

My 3 speed bicycles enjoy some of the best chain life of any of my bikes, my winter bike sees some extremely harsh use and after 3500 miles there is no measurable wear and have had 3 speed chains run in excess of 10,000 miles under similarly brutal conditions.

The fixed drives are much the same as the 3 speeds as I use brakes and one of the factors to extending a chain's life is cleaning and if you ride in wet or snowy conditions, really good fenders will do more than cleaning to extend your chain life. A little moisture will not hurt a well lubed chain but the crud that your wheels throw into the drive is full of grit and will drastically shorten chain life.

Chains and cassettes are designed to be consumables, it is sad but true.