Challenging Problem: Motion with Constant Velocity

Suppose that you have a friend who has been taking flying lessons and has just earned her pilot's license. In celebration, your friend offers to fly you from Dukesville where you live to New Otis, a town located 240 miles to the north. She explains that she has discovered a quaint new restaurant there that she would like to take you to. You agree to her plan, and you both take off for New Otis. For the first 120 miles of the trip your friend maintains a constant speed of 240 miles per hour, and for the second half of the trip you fly at 360 mph. How long does it take you to fly from Dukesville to New Otis?

(Hint: A good place to start is by making a drawing and by writing down known information.)