Graph Algorithms · Challenge problem

A project's activities are arcs in a directed network from start event $1$ to finish event $7$: $1\to2{:}5, 1\to3{:}3, 1\to4{:}6, 2\to5{:}4, 3\to5{:}7, 3\to6{:}5, 4\to6{:}2, 5\to7{:}3, 6\to7{:}6$ (days). Every activity leaving an event can start only once ALL activities entering that event are finished, and the project takes as long as its critical (longest) path, which is $14$ days. Activity $2\to5$ is NOT on the critical path. By how many days could activity $2\to5$ be delayed (started late) without delaying the project's overall finish time?