The scenario you described, where two quarks are separated by a distance of 100 km faster than the time scale of the strong force, would result in a highly hypothetical and extreme situation. The energy required to separate quarks by such a large distance would be tremendous.
In quantum chromodynamics (QCD), which is the theory that describes the strong force and interactions between quarks, quarks are confined within particles called hadrons due to the strong force. The strong force becomes increasingly stronger as quarks are pulled apart, making it more difficult to separate them.
To estimate the energy required to separate the quarks, we can consider the energy required to overcome the strong force and move them apart. However, it is important to note that the strong force is not a simple potential with a fixed energy cost for separation, as it increases with distance.
In this extreme scenario, where the quarks are separated by 100 km, far beyond the range of the strong force, the energy required would be astronomically high. Unfortunately, it is not possible to provide a precise numerical value without making significant assumptions and simplifications that may not be valid.
Moreover, it is important to mention that the concept of inflation, which is a theoretical framework used to explain the observed large-scale homogeneity and isotropy of the universe, operates on a cosmological scale and is not directly applicable to individual quarks within the context of the strong force.
In summary, the energy required to separate quarks by 100 km in such a short time and against the strong force would be extremely large, but an accurate numerical estimation is challenging due to the complex nature of the strong force and the extreme scenario described.