Earlier quoted context omitted.
If my math is correct, we would already need to build a spaceship that can travel at 1/10th the speed of light to reach Voyager 1 within one week. It will be quite an engineering challenge for the future.
https://science.nasa.gov/mission/voyager/where-are-they-now/ says the furthest is 24.4 million km from earth. Pulling out the trusty qalculator: $ qalc '24.4e6 km / 1 week / c to %' (((24.4 * (10^6)) kilometers) / (1 week)) / SpeedOfLight = approx. 0.0134572816% So this is using the "millions of kilometers per week" as a speed unit (like km/h but bigger), then dividing by the speed of light (c) to get the fraction of…
Wolfram Alpha also yields approx. 0.134 c for 1 week of travel time:
https://www.wolframalpha.com/input?i=distance+to+voyager+1+÷...
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Perhaps targeting 100 weeks of travel time would be more plausible:
https://www.wolframalpha.com/input?i=distance+to+voyager+1+÷...
0.00134 c is approx. two times the top speed of 0.00064 c for the fastest space probe:
https://en.wikipedia.org/wiki/Parker_Solar_Probe
If only we could harness gravity assist at will…