Answer:
14.86 knots.
Step-by-step explanation:
Given that:
The boats leave the port at noon.
Speed of boat 1 = 12 knots due east
Speed of boat 2 = 8 knots due south
At 2 pm:
Distance traveled by boat 1 = 24 units due east
Distance traveled by boat 2 = 16 units due south
Now, speed of boat 1 changes to 9 knots:
At 3 pm:
Distance traveled by boat 1 = 24 + 9= 33 units due east
Distance traveled by boat 2 = 16+8 = 24 units due south
Now, speed of boat 1 changes to 8+7 = 15 knots
At 5 pm:
Distance traveled by boat 1 = 33 + 2[tex]\times[/tex] 9= 51 units due east
Distance traveled by boat 2 = 24 + 2 [tex]\times[/tex] 15 = 54 units due south
Now, the situation of distance traveled can be seen by the attached right angled [tex]\triangle AOB[/tex].
O is the port and A is the location of boat 1
B is the location of boat 2.
Using pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units[/tex]
so, the total distance between the two boats is 74.28 units.
Change in distance per hour = [tex]\dfrac{Total\ distance}{Total\ time}[/tex]
[tex]\Rightarrow \dfrac{74.28}{5} = 14.86\ knots[/tex]
