Today people increasingly have the opportunity to opt-in to "usage-based" automotive insurance programs for reducing insurance premiums. In these programs, participants install devices in their vehicles that monitor their driving behavior, which raises some privacy concerns. Some devices collect fine-grained speed data to monitor driving habits. Companies that use these devices claim that their approach is privacy-preserving because speedometer measurements do not have physical locations. However, we show that with knowledge of the user's home location, as the insurance companies have, speed data is sufficient to discover driving routes and destinations when trip data is collected over a period of weeks. To demonstrate the real-world applicability of our approach we applied our algorithm, elastic pathing, to data collected over hundreds of driving trips occurring over several months. With this data and our approach, we were able to predict trip destinations to within 250 meters of ground truth in 10% of the traces and within 500 meters in 20% of the traces. This result, combined with the amount of speed data that is being collected by insurance companies, constitutes a substantial breach of privacy because a person's regular driving pattern can be deduced with repeated examples of the same paths with just a few weeks of monitoring.