Discolored water like you describe can also be from an old water heater and/or water that's been in the lines for a long time. If the house has sat vacant and you fire up each fixture to test it, you are essentially clearing each of the lines.

Often times, once it's cleared it's weeks or months before it comes back. I can't recall ever seeing it just run brown for more than a few minutes. Usually, much less.

As with the general consensus, the pipes are past their typical service life and replacement should be planned for. I have a comment about this - Generally poor performance (leakage, inconsistnet flow, etc) is common with materials of this age and should be expected until these pipes are replaced.