Answer
9mph
Work Step by Step
We first have to make a formula. One boat went speed X for 2 hours so we have $2x$ and the other went an additional 3 for 2 hours so we have $2(x+3)$. and the distance between them, the hypotenuse of the triangle is $30$ miles. So we will use the Pythagorean Theorem to build our formula.
$A^2+B^2 = C^2$
$(2x)^2+(2(x+3))^2 = 30^2$
$4x^2+(2x+6)^2 = 900$
$4x^2+4x^2+24x+36 = 900$
$4x^2+4x^2+24x+36 = 900$
$8x^2+24x+36 = 900$
Now let's move everything over to one side so we can use the quadratic formula:
$8x^2+24x-864 = 0$
Great then we just plug this into the quadratic formula for the answer:
$x = \frac{-24\frac{+}{-}\sqrt (24^2-(4*8*-864))}{2*8}$
$x = \frac{-24\frac{+}{-}\sqrt (576-(-27648))}{16}$
$x = \frac{-24\frac{+}{-}\sqrt (28224)}{16}$
$x = \frac{-24\frac{+}{-}168}{16}$
so we get our two answers:
$x = \frac{-192}{16}$ = -12
and
$x = \frac{144}{16}$ = 9
We know that we have to have a positive number for this problem so our answer is 9.
