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It's more or less impossible to answer this, since it depends on the exact route taken. It may give you some idea to know that it took the Voyager 2 spacecraft about 12 years to make the trip, though the scientists who planned it did not do so to optimize the travel time to Neptune specifically (it also visited several other planets first... that said, this probably didn't adversely impact the travel time too much).

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14y ago

What else can I help you with?