If piston A is pushed down 6 inches, how far will piston B move up?

To determine how far piston B will move up when piston A is pushed down 6 inches, we need to consider the principle of hydraulic systems, specifically Pascal's Law. In a hydraulic system, the force applied to a fluid in a confined space produces an equal and opposite force throughout the fluid.

If piston A is connected to piston B via a hydraulic fluid, the movement of one piston will have a corresponding effect on the other due to the incompressibility of the fluid. The ratio of the areas of the two pistons determines how far each will move in response to the movement of the other.

In this case, if the area of piston A is larger than that of piston B, then pushing piston A down will cause piston B to move up by a proportionally smaller distance. If the area ratio happens to allow a calculated movement upwards of 3 inches when 6 inches of displacement occurs in Piston A, then it follows that piston B will move up 3 inches as a direct result of that compression.

Thus, the answer that indicates piston B moves up 3 inches accurately reflects the mechanics of hydraulic systems, confirming the direct relationship between the movements of both pistons in accordance to their respective sizes and the pressures applied.