Answer:
13.695 m
Step-by-step explanation:
The assumption made here is that the boat/water interface is essentially frictionless, so that the center of mass of the system remains in the same place as the occupant of the boat moves around.
__
We can find the sum of the moments of boat and child about the pier end:
(46 kg)(7.6 m) + (80 kg)((7.6 +9.6/2) m) = 1341.6 kg·m
After the child moves, the center of mass of boat and child is presumed to remain in the same place. If x is the new distance from the pier to the child, the sum of moments is now ...
46x +80(x-4.8)* = 1341.6
126x -384 = 1341.6
x = (1341.6 +384)/126 = 13 73/105 ≈ 13.695 . . . meters
The child is about 13.695 meters from the pier when she reaches the far end of the boat.
_____
* The center of mass of the boat alone is half its length closer to the pier than is the child, so is located at x-4.8 meters.
