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At its most distant, when the two bodies are on the opposite sides of the sun from one another, Pluto lies 4.67 billion miles (7.5 billion kilometers) from Earth. At their closest, the two are only 2.66 billion miles (4.28 billion km) apart.
According to Wikipedia Pluto's minimum distance from the sun is 4.4billion km. The earth is at an average of 150 million km from the sun. Say the distance from earth to Pluto is about 4 250 000 000 000m. Not a terribly satisfactory answer (no one else has answered this yet) but I would guess about 9 years based on Voyager's current speed.