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Check out this link on experiments of relativity of time: Is there any practical proof for time dilation?
Take note of this text:
Plus GPS uses the theory of relativity in practical applications: GPS and Relativity
So yeah the gist is what if the speed of light changed so that it's a quarter of what it used to be. Imagine if you went on a flight and came back home and you'd see that everyone aged a month even though you were gone for only a few hours.
that's what happens to astronauts