Question 328202
There are various ways to go about this one. Here is one method.

From where she makes her 65 degree turn, extend a line straight out, then connect it to the point where she intersects the southwest line. 

This forms a right triangle. Draw a line from the intersection point back to where she turned. This forms another triangle.

Let the distance extended out from where she turned be x and the distance from there to the intersection point be 640+x (because southeast is 45 degrees from the origin)

The distance she flies is 320t.

Now, we can build two triangles and solve for t and x. t is what we really need.

{{{sin(25)=x/320t}}}

{{{x^2+(640+x)^2=(320t)^2}}}....[2]

{{{x=320t*sin(25)}}}....[3]

Sub [3] into [2] and solve for t.

{{{(320t*sin(25))^2+(640+(320t*sin(25)))^2=(320t)^2}}}

{{{204800sin^2(25)*t^2+409600sin(25)t+409600=102400t^2}}}

This is a quadratic to solve for t.

Doing so, gives us {{{t=4.13}}} hours.

The other solution is extraneous.