After introducing first passage percolation, we consider two such processes spreading at different rates on a graph G with bounded degree. One of them starts from a single source, while the other one starts (in a delayed manner) from countably many seeds distributed according to a product of iid Bernoulli random variables on the set of vertices. We consider several questions, focusing on the case where G is a non-amenable hyperbolic graph. This talk is based on joint works with Alexandre Stauffer.