It is highly challenging to simultaneously achieve high-rate and low-latency in live video streaming. Chunk-based streaming and playback speed adaptation are two promising new trends to achieve high user Quality-of-Experience (QoE). To thoroughly understand their potentials, we develop a detailed chunk-level dynamic model that characterizes how video rate and playback speed jointly control the evolution of a live streaming session. Leveraging on the model, we first study the optimal joint video rate-playback speed adaptation as a non-linear optimal control problem. We further develop model-free joint adaptation strategies using deep reinforcement learning. Through extensive experiments, we demonstrate that our proposed joint adaptation algorithms significantly outperform rate-only adaptation algorithms and the recently proposed low-latency video streaming algorithms that separately adapt video rate and playback speed without joint optimization. In a wide-range of network conditions, the model-based and model-free algorithms can achieve close-To-optimal trade-offs tailored for users with different QoE preferences.