1. **Problem statement:** A ship sails 20 km east from port P, then 25 km south, then 30 km east to reach point Q. 2. **Find the total distance sailed from P to Q:** The ship sails three legs: 20 km east, 25 km south, and 30 km east. Total distance sailed = $20 + 25 + 30 = 75$ km. 3. **Find the straight-line distance from P to Q:** We need to find the direct distance from P to Q, which is the hypotenuse of a right triangle formed by the east and south displacements. East displacement total = $20 + 30 = 50$ km. South displacement = $25$ km. Using the Pythagorean theorem: $$d = \sqrt{50^2 + 25^2}$$ $$d = \sqrt{2500 + 625}$$ $$d = \sqrt{3125}$$ $$d = 25\sqrt{5} \approx 55.9 \text{ km}$$ 4. **Explanation:** The ship's path forms a right triangle with legs 50 km (east) and 25 km (south). The direct distance from P to Q is the hypotenuse, calculated using the Pythagorean theorem. **Final answers:** - Total distance sailed: 75 km - Distance from P to Q: approximately 55.9 km