Existing black box explainability tools for object detectors rely on multiple calls to the model, which prevents them from computing explanations in real time. In this paper we introduce IncX, an algorithm for real-time incremental approximations of explanations, based on linear transformations of saliency maps. We implement IncX on top of D-RISE, a state-of-the-art black-box explainability tool for object detectors. We show that IncX's explanations are comparable in quality to those of D-RISE, with insertion curves being within 8%, and are computed two orders of magnitude faster that D-RISE's explanations.