SOLUTION: 2 ships leave port one sailing east and the other south. some time later they are 17 mi apart, with the eastbound ship 7 mi farther from the port than the southbound ship. how far

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Question 105761This question is from textbook structure and method book2
: 2 ships leave port one sailing east and the other south. some time later they are 17 mi apart, with the eastbound ship 7 mi farther from the port than the southbound ship. how far is each from port?
I thank you very much for your assistance. I constantly struggle with all of my word problems.
Once again your time and assistance is appreciated.
Sincerely,
Steph This question is from textbook structure and method book2

Answer by kmcruz09(38) About Me  (Show Source):
You can put this solution on YOUR website!
2 ships leave port one sailing east and the other south. some time later they are 17 mi apart, with the eastbound ship 7 mi farther from the port than the southbound ship. how far is each from port?
In this type of questions, we have to use the Pythagorean Theorem. It states that in a right triangle, the square of the first leg plus the square of the sqcond lerg is equal to the square of the hypotenuse. In this case, let us assume that x is the distance of the southbound ship from the port, then it follows that x + 7 is the distance of the eastbound ship from the port. They are 17 miles apart. Equating we have:
x%5E2+%2B+%28x%2B7%29%5E2+=+17%5E2
Solving:
x%5E2+%2B+x%5E2+%2B+14x+%2B+49+=+289
2x%5E2+%2B+14x+-+240+=+0
Applying the quadratic formula x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+,
we have:
x+=+%28-14+%2B-+sqrt%28+14%5E2-4%2A2%2A-240+%29%29%2F%282%2A2%29+
Solving:
x+=+%28-14+%2B-+sqrt%28+196-%28-1920%29%29%29%2F%284%29+
x+=+%28-14+%2B-+sqrt%28+2116%29%29%2F%284%29+
x+=+%28-14+%2B+46+%29%2F%284%29+ or x+=+%28-14+-+46+%29%2F%284%29+
x+=+%2832%29%2F4 or x+=+-60%2F4
x=8 or x=-15
Since we are solving real problems, it cannot be a negative integer. So we have to use the positive root which is x=8
Then the distance of the southbound ship from the port is 8 miles, while the distance of the eastbound ship from the port is 15 miles.
Thank you.
~kmcruz09~