  We extend the core-accretion model of giant gaseous planets by Pollack et al.
(\cite{P96}) to include migration, disc evolution and gap formation. Starting
with a core of a fraction of an Earth's mass located at 8 AU, we end our
simulation with the onset of runaway gas accretion when the planet is at 5.5 AU
1 Myr later. This timescale is about a factor ten shorter than the one found by
Pollack et al. (\cite{P96}) even though the disc was less massive initially and
viscously evolving. Other initial conditions can lead to even shorter
timescales. The reason for this speed-up is found to result from the fact that
a moving planet does not deplete its feeding zone to the extend of a static
planet. Thus, the uncomfortably long formation timescale associated with the
core-accretion scenario can be considerably reduced and brought in much better
agreement with the typical disc lifetimes inferred from observations of young
circumstellar discs.
