Saving Time with Different Flight Routes and Wind Velocity

[leafs]

Homework Statement

A passenger has to options to get to his desired city. The cheaper option is to travel 1200km east, then catch a connecting flight with a 30 min stop over that would take him 350km south. The expensive option is to fly directly to the city. If all three airplanes travel at 345km/h, and the wind is a constant 45km/h (S35degrees W), how much time does the passenger save by taking the expensive option?

Homework Equations

The Attempt at a Solution

I can't come up with a solution. I don't know what to do

 

[dioib]

I think the problem wants you to assume the Airplanes have that speed relative to the air that is itself moving; if so, you need to subtract the projection of the wind velocity along the flight direction and that is going to give you the actual speed for each specific flight (that makes a particular angle of its own with the wind velocity) in the Earth frame. Including the stop time, you need to figure out the time (having found the velocity) for each specific flight and figure out the total for the two routes. You also need to assume that people seating next to you are reasonably normal, otherwise the real life answer is going to be much longer in extent..