  We present new analysis from the GEEC2 spectroscopic survey of galaxy groups
at $0.8<z<1$. Our previous work revealed an intermediate population between the
star-forming and quiescent sequences and a strong environmental dependence in
the fraction of quiescent galaxies. Only $\sim5$ per cent of star-forming
galaxies in both the group and field sample show a significant enhancement in
star formation, which suggests that quenching is the primary process in the
transition from the star-forming to the quiescent state. To model the
environmental quenching scenario, we have tested the use of different
exponential quenching timescales and delays between satellite accretion and the
onset of quenching. We find that with no delay, the quenching timescale needs
to be long in order to match the observed quiescent fraction, but then this
model produces too many intermediate galaxies. Fixing a delay time of 3 Gyr, as
suggested from the local universe, produces too few quiescent galaxies. The
observed fractions are best matched with a model that includes a delay that is
proportional to the dynamical time and a rapid quenching timescale ($\sim0.25$
Gyr), but this model also predicts intermediate galaxies H{\delta} strength
higher than that observed. Using stellar synthesis models, we have tested other
scenarios, such as the rejuvenation of star formation in early-type galaxies
and a portion of quenched galaxies possessing residual star formation. If
environment quenching plays a role in the GEEC2 sample, then our work suggests
that only a fraction of intermediate galaxies may be undergoing this transition
and that quenching occurs quite rapidly in satellite galaxies ($\lesssim0.25$
Gyr).
