Oldest solved cold case?

[md2000]

This isn’t quite so old, but recent:

Published on Sep 13, 2017
A cold case that has kept investigators up at night for four decades all but came to a close with one man’s guilty plea. Lloyd Welch, a 60-year-former carnival worker entered the plea in court 42 years after the disappearance of Katherine and Sheila Lyon. The girls vanished in 1975 from a suburban Maryland mall. Welch was sentenced to 48 years in prison as part of a plea agreement with prosecutors. InsideEdition.com’s Leigh Scheps (http://twitter.com/LeighTVReporter) has more.

Wendy Jo Halison's murderer was dead 4 years by the time the case was solved, according to OP article. (1968-2017 - 49 years)