Not literally in a sense that it must go in same direction as they went, but in distance to Earth.
I understand that this question may be a bit vague (is the budget 500M or 5B?) so feel free to assume: large budget: tens of billions.
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With reasonably current technology there are basically three options, I think:
In all cases, I think, the answer would be a few decades.
If you are really in a hurry you could consider the "nuclear shotgun", perhaps on the Moon. That could launch a reasonably large, very tough payload at a very high initial velocity.