An analytic model for the relation between the star-forming fraction of the total gas mass (f_sf) and the gas depletion time (t_depl) reproduced from Semenov et al. (2018, Fig. 7). The grids show the predicted f_sf and t_depl for various values of the star-formation efficiency per free-fall time (ε_ff; how much of the gas is converted to stars on a cloud dynamical time), and the boost factor of momentum gain per supernova (b). We only show the b-values for the red grid lines. The key parameters of this model are the timescale for gas to become star-forming (τ₊) and the timescale for the star-forming gas to be rendered non-star forming (τ_−, d). The blue grid is for local disk galaxies with long τ₊ (400 Myr) and the high ratio of τ₊/τ_−, d (5). The red grid shows the case where τ₊ is short (10 Myr) and τ₊/τ_−, d is low (0.1). It is apparent that local disk galaxy models are inconsistent with the short t_depl (⩽100 Myr) observed in the three high redshift radio galaxies including PKS 0529-549. Gas compression can shorten t_depl by reducing τ₊ (therefore low τ₊/τ_−, d), resulting in high f_sf, i.e., high dense molecular gas fraction.