Energy efficiency and timeliness (i.e., predictable job latency) are two essential – yet opposing – concerns for embedded systems. Hard timing guarantees require conservative resource allocation while energy minimization requires aggressively releasing resources and occasionally violating timing constraints. Recent work on approximate computing, however, opens up a new dimension of optimization: application accuracy. In this paper, we use approximate computing to achieve both hard timing guarantees and energy efficiency. Specifically, we propose MEANTIME: a runtime system that delivers hard latency guarantees and energy-minimal resource usage through small accuracy reductions. We test MEANTIME on a real Linux/ARM system with six applications. Overall, we find that MEANTIME never violates real-time deadlines and sacrifices a small amount (typically less than 2%) of accuracy while reducing energy to 54% of a conservative, full accuracy approach.