Question 618866: two boats leave a marina. one travels east. and the other travels south after 30 min the second boat has traveled one mile farther then the first boat and the distance between the boats is five miles. find the distance each has traveled
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! two boats leave a marina. one travels east. and the other travels south after 30 min the second boat has traveled one mile farther then the first boat and the distance between the boats is five miles. find the distance each has traveled
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Draw a coordinate system.
The eastbound boat stops at (x,0)
The southbound boat stops at (0,y)
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Equation:
y = x+1
Distance Equation:
sqrt[x^2 + y^2] = 5
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Substitue for "y" and solve for "x":
sqrt[x^2 + (x+1)^2] = 5
x^2 + x^2 + 2x + 1 = 25
2x^2 + 2x -24 = 0
x^2 + x - 12 = 0
Factor:
(x+4)(x-3) = 0
x = 3 miles (eastbound distance)
x+1 = 4 miles (southbound distance)
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Cheers,
Stan H.
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