We study the jamming transition in a model of elastic particles under shear at zero temperature, with a focus on the relaxation time τ1. This relaxation time is from two-step simulations where the first step is the ordinary shearing simulation and the second step is the relaxation of the energy after stopping the shearing. τ1 is determined from the final exponential decay of the energy. Such relaxations are done with many different starting configurations generated by a long shearing simulation in which the shear variable γ slowly increases. We study the correlations of both τ1, determined from the decay, and the pressure, p1, from the starting configurations as a function of the difference in γ. We find that the correlations of p1 are longer lived than the ones of τ1 and find that the reason for this is that the individual τ1 is controlled both by p1 of the starting configuration and a random contribution which depends on the relaxation path length - the average distance moved by the particles during the relaxation. We further conclude that it is γτ, determined from the correlations of τ1, which is the relevant one when the aim is to generate data that may be used for determining the critical exponent that characterizes the jamming transition.