I dont understand how to set this up

Question

The cruising speed of an airplane is 150 miles per hour. You plan to hire the plane for 3 hour sightseeing trip. You instruct the pilot to fly north as far as she can and still return to the airport at the end of the allowed time. How far north should the pilot fly if the wind is blowing from the north at 30 miles per hour.

Answer 1

This problem gives you a total time that you need to limit yourself to, so you will have to add the times of each leg of the trip and solve. Generally, d = r * t, and you can rewrite this as t = d / r. Since the plane is traveling due north on the way out, and due south on the way home, the distances of each leg will be equal. Because there is a south-blowing wind, the plane will travel more slowly on the way north than it does south.

 

Going north, the plane flies at 150-30 = 120 mph due to the headwind.

Going south, the plane flies at 150+30 = 180 mph due to the tailwind.

 

The total time traveled is therefore:

d / 120 + d / 180 = 3

 

Multiply everything by the LCD (360), and you should be able to solve for d!