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The highest warp speed that a Federation starship has traveled at safely was warp 9.975 by the USS Voyager. That is along the lines of 6000 times the speed of light, nearly 4 times that of warp 9. Voyager can achieve that speed under its own power, but it can only remain at that speed for up to 12 hours at a time, so the majority of their journey was traveling at warp 9.

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