Voyager 1 was launched on Sept 5, 1977 and encountered Jupiter March 5, 1979, a journey of less than 2 years. When I try to calculate the trajectory of the probe I assume a Hohmann transfer from Earth to Jupiter even if I'm not 100% about that (the Internet doesn't have a lot of information on that point).
The thing is, when I compute the theoretical time of flight with the following formula:
$$time = \pi*\sqrt{\frac{a^3}{\mu_{sun}}}$$
with $a$ the semi-major axis and $\mu_{sun}$ the standard gravitational parameter
$$a=(149598023+778298361)/2 $$
$$\mu_{sun} = 1.32712428e11$$
I find $time=2.7$ years
But in reality Voyager managed to reach Jupiter in less than 2 years so how is that possible? I thought about the velocity gained by the probe from the Titan 3E rocket which certainly played a role. But how can I integrate this velocity in the time formula?