A 12-ft ladder is leaning against a vertical wall when Jack begins pulling the foot of the ladder away from the wall at a rate of 0.2 ft/s. What is the configuration of the ladder at the instant when the vertical speed of the top of the ladder equals the horizontal speed of the foot of the ladder?

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1. Identify the relationship between the lengths of the ladder, the height of the top of the ladder on the wall (y), and the distance from the wall to the foot of the ladder (x) using the Pythagorean theorem: x^2 + y^2 = 12^2.
2. Differentiate the Pythagorean theorem equation with respect to time to relate the rates of change of x and y: 2x(dx/dt) + 2y(dy/dt) = 0.
3. Substitute the known rate of change for the foot of the ladder (dx/dt = 0.2 ft/s) into the differentiated equation to express dy/dt in terms of x and y.
4. Set dy/dt equal to dx/dt (0.2 ft/s) to find the specific configuration of the ladder when the vertical speed equals the horizontal speed.
5. Solve the resulting equations to find the values of x and y at the instant when the speeds are equal, ensuring to check that the values satisfy the original Pythagorean theorem.