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The speed of light is a constant because no matter how fast a person is travelling toward a beam of light that is moving away from them, that beam of light always travels at a constant speed away from the person.
For example, if I were to throw a baseball 50 mph, then ran after it at 25 mph, the ball is in effect moving away from me at 25 mph and I would eventually catch up with the ball.
If I shine light away from me at 300,000 kps, then run after it at 150,000 kps, it is still moving aways from me at 300,000 kps.
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de omnibus dubitandum est
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