Question 504075: Mary works due north of home. Her husband Juan works due east. They leave for work at the same time. By the time Mary is 5 miles from home, the distance between them is 1 mile more than Juan’s distance from home. How far from home is Juan.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Mary can be viewed as driving up the y-axis to the point (0,5).
Juan is driving along the x-axis.
The diagonal line from (0,5) to (0,x) is "1 more than Juan's distance from home."
So the diagonal line is of length x+1.
Of course, this diagonal line is the hypotenuse.
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Using the Pythagorean Theorem...
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(x+1)^2 = x^2 + 25
x^2 + 2x + 1 = x^2 + 25
subtract x^2 from both sides
2x + 1 = 25
subtract 1 from both sides
2x = 24
divide both sides by 2
x = 12
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Juan is 12 miles from home.
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Always check your work.
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c^2 = 13^2 = 169
x^2 = 12^2 = 144
y^2 = 5^2 = 25
169 = 144+25
Correct.
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Answer: Juan is 12 miles from home.
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Done.
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