Problem $1$:

Assuming we have $5$ different airports scattered in different locations, some of those airports are connected to other airports with a line, such that we could travel along the line to go from one airport to another. But not all lines have the same travel time. Some lines may take more travel time than others, while others may take less.

The problem is$,$ what's the shortest time we can get to travel from Airport A to Airport D$?$

$($This is a specific example of a more general problem in graph theory, where we have vertices, in this case, our airports, that are connected by edges, in this case, our lines. Together, these vertices and edges form a graph, and in particular, this graph is a weighted graph because each edge has some value to indicate how costly it is to travel along that edge.$)$