We use borehole strain and seismic data to show that slow slip and tremor in central Cascadia are correlated on a range of time scales shorter than 1 day. The recorded strain rate is our proxy for the slow slip moment rate, and the seismic amplitude is our proxy for the tremor amplitude. We find that, on average, the strain rate is higher when the seismic amplitude is larger. This correlation persists on time scales between 15 min and 16 h, and it can be seen in each of the five slow slip events between 2007 and 2011. Our results imply that the slow slip moment rate varies by a large amount even at these short time scales. For instance, we observe a factor of 2 variation on time scales shorter than 4 h. This apparently aperiodic variation is larger than the previously observed variation in moment rate resulting from tidal forcing. It is a lower bound on the actual moment rate variation, as we detect only changes in slow slip that are correlated with tremor amplitude.