Answer:
The boats cross paths at the points (1,8) and (4,11)
Explanation:
First, we want to find the points of intersection between the two paths. We are given two equations, both in the form y=(equation). Since we want to find the intersection points, we set the two equations equal to each other (since both equal y we can plug one of the equations in for y into the other equation) to get
-x^2+6x+3=x+7
From here, we solve this like a normal quadratic equation, move all variables to one side first
-x^2+5x-4=0
This factors to -(x-1)(x-4)=0, giving us x=1 and x=4
Now we plug these back into one of the original equations (in this case the linear equation is much more simple) to give us the points (1,8) and (4,11)