Ah, a math word problem! Let's see if we can solve it together.

We have a plane flying against a steady headwind for 720 miles, and then it returns to the same point with the wind. We're given that the entire trip takes 10 hours.

To solve this problem, let's first find out how long it takes for the plane to fly against the headwind.

Let's call the speed of the plane in still air "p" and the speed of the wind "w". Since distance equals speed multiplied by time (d = s * t), we can set up two equations based on this information:

Equation 1: (p - w) * t1 = 720 (representing time and speed against headwind)

Equation 2: (p + w) * t2 = 720 (representing time and speed with tailwind)

Since we don't know either "t1" or "t2," let's solve for them in terms of p and w:

t1 = 720 / (p - w)

t2 = 720 / (p + w)

Now, from what is given in the problem, we know that:

t1 + t2 = 10

Substituting our expressions for t1 and t2 into this equation:

(720 / (p - w)) + (720 / (p + w)) = 10

To make things clearer, let's multiply both