Question 524836
The boats are travelling at right angles

At any given time if you draw a line from the starting point to the boats and draw a line joining the two boats they form a right triangle

distance = 10 miles this is the hypotenuse 

let west bound boat be at x miles from starting point
other boat is x+2 miles from origin

x^2+(x+2)^2=10^2

x^2+x^2+4x+4=100
2x^2+4x-96 = 0
/2
x^2+2x-48=0
x^2+8x-6x-48=0
x(x+8)-6(x+80=0
(x+8)(x-6)=0
S0 x=6 

west bound boat is 6 miles
North bound boat is 8 miles  from origin