Actually we already have! The amazing spacecraft Voyager 1, launched in 1977, already left the Solar System. (Of course it depends alot on how you define the edge of the Solar System.) See its story here http://voyager.jpl.nasa.gov/
I was lucky enough to visit the Jet Propulsion Labs in 1985 and talk to someone preparing an experiment ready for when Voyager reached the planet Uranus.
Well, the Voyager 1 probe, which was launched before I was born, is now heading to the outer reaches of our system, so not too long! Check out NASA’s site for more details.
A very long time! At present, cost is an overriding factor. It is cheaper to use robotic probes than it is to boost all the necessary supplies to keep a person alive for several years while the mission is in progress.
The other problem with space flight is time!! It would take years just to travel to the boundary of our solar system and what then?
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