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 \sim 5 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 ( \sim 0.25 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 ( \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle < $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 0.25 Gyr ) .