This year during Christmas you would like to invite your best friend, who recently had a surgery, to come and visit and celebrate the occasion with you. However, your friend is a student in another country now and does not have lots of money to pay for costly flight tickets during the peak season. Therefore, you decide to help your friend by paying a portion of the ticket. Both of you began the search for ticket and draw the graph below showing the routes from origin $($O$)$ to destination $($D$),$ which is your town. Since your friend had a surgery you prefer to have a shortest flight time. $($a$)$ If this is a shortest path problem, what acts as distance in this problem? $($b$)$ what is the shortest path and how long does it take $($please clearly show how you did the calculations for obtaining the answer$).$