Question 840288: Two ships start out the same point. One ship travels X miles directly due east, and the other ship travels X miles directly due south. The ship that is traveling to the East travels another 7 miles in the easterly direction, while the other, southerly traveling ship, travels an additional 15 miles south, in the same period of time. What distance X did the ships travel initially, if there distance from each other in the end is 51.22 miles?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Two ships start out the same point.
One ship travels X miles directly due east, and the other ship travels X miles directly due south.
The ship that is traveling to the East travels another 7 miles in the easterly direction, while the other, southerly traveling ship, travels an additional 15 miles south, in the same period of time.
What distance X did the ships travel initially, if there distance from each other in the end is 51.22 miles?
:
Use pythag; a^2 + b^2 = c^2, where
a = (x+7)
b = (x+15)
c = 51.22
:
(x+7)^2 + (x+15)^2 = 51.22^2
FOIL, square 51.22
x^2 + 14x + 49 + x^2 + 30x + 225 = 2623.5
combine like terms
2x^2 + 44x + 49 + 225 - 2623.5 = 0
a quadratic equation
2x^2 + 44x - 2349.5 = 0
Using the quadratic formula, a positive solution round out to:
x = 25 mi
:
:
Check this, ship one traveled 32 mi, ship two traveled 40 mi
Using a calc 
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