Consider the first passage percolation distance on random planar maps, which is obtained by putting i.i.d. exponential random lengths on each (dual) edge. The study of this distance is often simpler than the study of the (dual) graph distance. I will describe a time-reversal of the uniform peeling exploration, which enables me to obtain the scaling limit of the number of faces along the geodesics to the root, to compare the metric balls for the first passage percolation and the dual graph distance and to upperbound the diameter of large random maps. Then, I will obtain the scaling limit of the tree of first passage percolation geodesics to the root via a stochastic coalescing flow of pure jump diffusions. This stochastic flow is also a tool to construct some random metric spaces which I conjecture to be the scaling limit of random planar maps with high degrees.