Question 420202
Farthest distance = 600 miles will be the hypotenuse

the balance 800 is the sum of the two legs of the right triangle.
if one side is x
other side = 800-x
..
x^2+(800-x)^2=600^2

x^2+640000-1600x+x^2=360000
2x^2-1600x+280000=0
/2
x^2-800x+140000=0
solve using quadratic equation
b^2-4ac= 120000
one side = 541.4 miles
other side =258.6 miles