Answer
The boat moves a distance of 0.46 meters in the direction of the 85-kg person's original location.
Work Step by Step
Let $x=0$ be the point where the 85-kg person is sitting.
We can find the center of mass of the boat with two people:
$x_{CM} = \frac{(55~kg)(3.0~m)+(58~kg)(1.5~m)}{85~kg+55~kg+58~kg}$
$x_{CM} = 1.27~m$
The center of mass is 1.27 meters from the 85-kg person.
Since there is no net external force acting on the system, the center of mass will stay at rest at the same location relative to the water. However, after the people in the boat change positions, the center of mass will be 1.27 meters from the 85-kg person. Since the physical location of the center of mass does not move, the boat must move a certain distance.
From simple geometry, we can see that the 85-kg person is sitting a distance of 2.54 meters from his original location, on the other side of the center of mass. Therefore, the boat must have moved a distance of (3.0 m - 2.54 m), which is 0.46 meters, in the direction of the 85-kg person's original location.
