Question 329049
let southbound ship be at x miles from port
the other will be (x+7) miles from the port east.
they form a right triangle
x^2+(x+7)^2=17^2
x^2+x^2+14x+49=289
2x^2+14x=289-49
2x^2+14x=240
divide by 2
x^2+7x=120
x^2+7x-120=0
x^2+15x-8x-120=0
x(x+15)-8(x+15)=0
(x+15)(x-8)=0
x= -15 or x = 8 ignore negative value.
x=8  miles south bound ship from port
x+7 = 8+7 =15 miles distance of the east bound ship from port