Modern speech processing systems rely on self-attention. Unfortunately, token mixing with self-attention takes quadratic time in the length of the speech utterance, slowing down inference and training and increasing memory consumption. Cheaper alternatives to self-attention for ASR have been developed, but they fail to consistently reach the same level of accuracy. This paper, therefore, proposes a novel linear-time alternative to self-attention. It summarises an utterance with the mean over vectors for all time steps. This single summary is then combined with time-specific information. We call this method "SummaryMixing". Introducing SummaryMixing in state-of-the-art ASR models makes it feasible to preserve or exceed previous speech recognition performance while making training and inference up to 28% faster and reducing memory use by half.