SOLUTION: There are two ships, one travels south and one travels east. Several hours after departure two ships are 340 miles apart. If the ship traveling south traveled 140 miles farther tha

Question 325198: There are two ships, one travels south and one travels east. Several hours after departure two ships are 340 miles apart. If the ship traveling south traveled 140 miles farther than the other, how many miles did each travel?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.

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