If you wanted to have a probe pass Voyager 1 in 10 years, you would need to launch it today and get it going 15.9 AU/year, which is blazing fast. Almost 5 times as fast as Voyager 1. New Horizon, if launched today, could almost do it (14.13 AU/year), but it's mission wasn't set up to leave it traveling as fast as Voyager 1. Although it's going out in the same direction and was launched faster, it will ultimately end up going slower.
If you give yourself 10 years to design the probe and something to get it going that fast, then the speed you actually need jumps up to 19.5 AU/year. The longer it takes you to design your fast rocket, the faster it has to go in order to catch Voyager 1 in the same amount of time.
Realistically, unless something exotic happens in space propulsion technology, we will never catch Voyager 1 within our lifetime. If we launched today at twice the speed of Voyager 1, then we could catch it in around 50 years, but that's not going to happen.
If you give yourself 10 years to design the probe and something to get it going that fast, then the speed you actually need jumps up to 19.5 AU/year. The longer it takes you to design your fast rocket, the faster it has to go in order to catch Voyager 1 in the same amount of time.
Realistically, unless something exotic happens in space propulsion technology, we will never catch Voyager 1 within our lifetime. If we launched today at twice the speed of Voyager 1, then we could catch it in around 50 years, but that's not going to happen.