The travel time map of a compact length space with a closed measurement set takes any point of the space to the function which measures the distance from this point to every point in the measurement set. The range of this map is called the travel time data, and it appears in the proofs of many geometric inverse problems. For instance, if the length space is a compact Riemannian manifold and the measurement set is the boundary of the manifold, the reconstruction of the travel time data is the essence of the celebrated boundary control method, used to recover a compact Riemannian manifold from its boundary spectral data. This problem is commonly known as the Gel’fand’s inverse boundary spectral problem. We provide a Lipschitz stability results for the travel time data, under certain geometric conditions. These geometric conditions are related to the question of when a geodesic in a length space is extendable. Further, we provide several examples of manifolds, with and without boundary, for which our geometric conditions are satisfied.