One of Speedy Airlines' flights is about to take off from Seattle for a nonstop flight to London. There is some flexibility in choosing the precise route to be taken, depending upon weather conditions. The following network depicts the possible routes under consideration, where SE and LN are Seattle and London, respectively, and the other nodes represent various intermediate locations.

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.