Question 325198
let x = the number of miles for the ship that traveled east.
let x+140 = the number of miles for the ship that traveled south.
You have a right triangle.
The hypotenuse is equal to 340 miles.
one leg equals x
the other leg equals x+140


using pythagorus, the equation for the right triangle is:


c^2 = a^2 + b^2

c = 340
a = x
b = x+140


this equation becomes:


340^2 = x^2 + (x+140)^2


this becomes:


115600 = x^2 + x^2 + 280x + 19600


subtract 115600 from both sides of this equation to get:


x^2 + x^2 + 280x + 19600 - 115600 = 0


combine like terms to get:


2x^2 + 280x - 96000 = 0


divide both sides of this equation by 2 to get:


x^2 + 140x - 48000 = 0


use quadratic formula to solve:


a = 1
b = 140
c = -48000


sqrt(b^2-4ac) = 460


x = (-b +/- sqrt(b^2-4ac))/2a


x = (-140 +/- 460)/2


x = -300 or x = 160


since x has to be positive, go with x = 160


you get:


c^2 = a^2 + b^2 which becomes:


340^2 = 160^2 + (160+140)^2 which becomes:


340^2 = 160^2 + 300^2 which becomes:


115600 = 115600 which is true confirming the value for x is good.


The ship traveling east traveled 160 miles.
The ship traveling south traveled 300 miles.