Two trucks leave a warehouse at the same time. One travels due north at an average speed of 48 miles per hour, and the other travels due south at an average speed of 49 miles per hour. After how many hours will the two trucks be 339.5 miles apart?

Step 1 ：Two trucks leave a warehouse at the same time. One travels due north at an average speed of 48 miles per hour, and the other travels due south at an average speed of 49 miles per hour.

Step 2 ：The two trucks are moving in opposite directions, so their speeds add up. The total speed is \(48 mph + 49 mph = 97 mph\).

Step 3 ：We can use the formula for distance, which is speed multiplied by time. We can rearrange the formula to solve for time, which is distance divided by speed.

Step 4 ：The distance is 339.5 miles. So, the time is \(\frac{339.5 miles}{97 mph}\).

Step 5 ：Final Answer: The two trucks will be 339.5 miles apart after \(\boxed{3.5}\) hours.