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Originally Posted by darkdev
According to GR, as speed increases, time slows.
I assume that speed is measured as motion across fixed space.
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The speed is not measured against any "fixed point". It is relative (hense, "Special Relativity"). The speed is measured against any other intertial frame of reference. This means there is no "other galaxy travelling slower" (paraphrasing) than us. Their speed is our speed, as we are just 2 frames of reference. Each galaxy might have a different relative speed as compared to a 3rd frame, but not to each other. A person in that 3rd frame of reference would indeed see time passing at different rates for each galaxy.