Question 258355: Starting at home, a man traveled 9 miles east, then 7 miles north, then 3 miles east, then x miles south. At that point, he was 13 miles from home. Find all possible values for x.
Found 2 solutions by Fombitz, stanbon:
Answer by Fombitz(32388)   (Show Source):
You can put this solution on YOUR website! Let east be positive X, north positive Y.
He starts at (0,0).
9 miles east: (0,0)+(9,0)=(9,0)
7 miles north: (9,0)+(0,7)=(9,7)
3 miles east:(9,7)+(3,0)=(12,7)
x miles south:(12,7)+(0,-x)=(12,7-x)
Use the distance formula,
 or 
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Starting at home, a man traveled 9 miles east, then 7 miles north, then 3 miles east, then x miles south. At that point, he was 13 miles from home. Find all possible values for x.
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Draw a picture.
Put the start at (0,0)
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9 east goes to (9,0)
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7 miles north goes to (9,7)
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3 miles east goes to (12,7)
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x miles south goes to (12,7-x)
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Equation:
Distance from (0,0) to (12,7-x)
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d = sqrt[(12-0)^2 +(7-x-0)^2] = 13
13 = sqrt[144 + 49 - 14x + x^2]
169 = 193 - 14x + x^2
x^2 - 14x + 24 = 0
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x = [14 +- sqrt(14^2 - 4*24)]/2
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x = [14 +- 10]/2
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x = 12 or x = 2
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Cheers,
Stan H.
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