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I was of the opinion that the 13.8 billion "years old" was calculated from the speed the light took to reach us from the farthest objects in the distance.
Correct me if I'm wrong.
Not really, or rather not fully. The age of the universe is calculated based on the cosmological constant cold dark matter model (in short the Lambda-CDM model). This model describes the evolution of the universe and explains why we see the stuff we see today, including the light from the most distant starts (or more correctly the light from their galaxies as we cannot separate the light from individual stars in very distant galaxies), the distribution of galaxies and dark matter/energy as well as the patterns in the 3K background radiation etc. The age of the universe is related to the cosmological constant. If you can determine the value of this constant, then you can determine the age of the universe. This is what the Lambda-CDM model does. I.e. it is little bit more complex than just dividing a distance with the speed of light since you need to take into account the expansion rate of the universe itself which is dependent on the (types of) energy content of the universe, such as the ration of dark energy v.s. energy which in itself change over time. Doing all this, and more, physicists has concluded that the age of the universe is 13.798 ± 0.037 billion years.
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