Question

Two boats leave the same marina. One heads north, and the other heads east. After some time, the northbound boat has traveled 16 miles, and the eastbound boat has traveled 12 miles. How far apart are the two boats?

Answer 1

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)

Explanation: