The winds along each arc greatly affect the flying time $($and so the fuel consumption$).$ Based on current

meteorological reports, the flying times $($in hours$)$ for this particular flight are shown next to the arcs.

Because the fuel consumed is so expensive, the management of Speedy Airlines has established a policy

of choosing the route that minimizes the total flight time.

$($a$)$ What plays the role of "distances" in interpreting this problem to be a shortest$-$path problem?

$($b$)$ Solve this shortest path problem by using Bellman's Algorithm.