Question 333494
the boats are sailing at a right angle to each other  (remember Pythagoras)


when the hypotenuse is 10 mi , one side is 2 mi longer than the other


a^2 + b^2 = c^2


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


x^2 + x^2 + 4x + 4 = 100 ___ 2x^2 + 4x - 96 = 0 ___ x^2 + 2x - 48 = 0


factoring ___ (x + 8)(x - 6) = 0


x = -8 ___ and ___ x = 6 ___ negative value NOT realistic


so the shorter distance (west) is 6 mi , and the longer distance (north) is 8 mi



FYI ___ this is a 3-4-5 triangle