Final answer:
The fishing boat traveled approximately 3.15 miles further than its original route.
Step-by-step explanation:
To determine how much further the fishing boat traveled than its original route, we need to calculate the total distance traveled on the detour compared to the distance of the original route.
The boat initially planned to travel in a straight line, but due to the storm, it had to change its course and travel 4 miles east and 9 miles south. This forms a right-angled triangle.
Using the Pythagorean theorem, we can find the length of the hypotenuse (the distance of the original route):
c² = a² + b²
c² = 4² + 9²
c² = 16 + 81
c² = 97
c = √97 ≈ 9.85 miles
The boat traveled approximately 9.85 miles on its original route.
To find the distance traveled on the detour, we can use the sum of the distances traveled east and south:
Detour distance = 4 miles + 9 miles = 13 miles
The boat traveled approximately 13 miles on the detour.
Therefore, the boat traveled approximately 13 - 9.85 = 3.15 miles further than its original route.