Congestion in urban areas causes financial loss to business and increased use of energy compared with free-flowing traffic. Providing citizens with accurate information on traffic conditions can encourage journeys at times of low congestion and uptake of public transport. Installing the measurement infrastructure in a city to provide this information is expensive and potentially invades privacy. Increasingly, public transport vehicles are equipped with sensors to provide real-time arrival time estimates, but these data are sparse. Our work shows how these data can be used to estimate journey times experienced by road users generally. In this paper we describe (i) what a typical data set from a fleet of over 100 buses looks like; (ii) describe an algorithm to extract bus journeys and estimate their duration along a single route; (iii) show how to visualise journey times and the influence of contextual factors; (iv) validate our approach for recovering speed information from the sparse movement data.