Take decades to catch up to the location of either voyager probe. The probes have be traveling for a long time. They have also taken advantage of a rare planetary alignment that allowed them to visit a lot of planets and get gravity assists from them (converting a tiny portion of the planet's angular momentum into orbital speed for the spacecraft)
Won't ion engines power by something like Kilopower reactor let us do better?
Bunch of napkin math: you'd need something like 10 kilowatts and 140 km/s detla-v to catch up to Voyager in a decade, assuming a New Horizons equivalent Earth escape velocity. The amount of xenon is technically possible, however even assuming impressive 8000 Isp thrusters, your fuel mass fraction ends up being 90+% fuel which doesn't leave a lot of mass for that reactor and radiators.
A 20 year intercept would be pretty reasonable though. It needs about 15 km/s delta v after that NH style escape, about a kilowatt of power, and maybe a 25% fuel mass fraction at 6000 Isp. That's all very reasonable by current standards.