Recent statistical methods fitted on large-scale GPS data are getting close to answering the proverbial "When are we there?" question. Unfortunately, current methods often only provide point predictions for travel time. Understanding travel time distribution is key for decision-making and downstream applications (e.g., ride share pricing decisions). Empirically, single road-segment travel time is well-studied, understanding how to aggregate such information over many segments to arrive at the distribution of travel time over a route is challenging. We develop a novel statistical approach to this problem, where we show that, under general conditions, without assuming a distribution of speed, travel time normalized by distance follows a Gaussian distribution with route-invariant population mean and variance. We develop efficient inference methods for such parameters, with which we propose population prediction intervals for travel time. Our population intervals are asymptotically tight and require only two parameter estimates. Using road-level information (e.g.~traffic density), we further develop a catered trips-specific Gaussian-based predictive distribution, resulting in tight prediction intervals for short and long trips. Our methods, implemented in an R-package, are illustrated in a real-world case study using mobile GPS data, showing that our trip-specific and population intervals both achieve the 95\% theoretical coverage levels. Compared to alternative approaches, our trip-specific predictive distribution achieves (a) the theoretical coverage at every level of significance, (b) tighter prediction intervals, (c) less predictive bias, and (d) more efficient estimation and prediction procedures that only rely on the first and second moment estimates of speed on edges of the network. This makes our approach promising for low latency large-scale transportation applications.