Answer
The canoe moves a distance of 1.29 meters.
Work Step by Step
Since there are no external forces acting on the system, the center of mass remains fixed. Let the left end of the canoe be the origin.
$x_{cm} = \frac{(45.0~kg)(1.00~m)+(60.0~kg)(2.50~m)}{105.0~kg}$
$x_{cm} = 1.857~m$
After the person walks to the new position, we can find the center of mass relative to the left end of the canoe.
$x_{cm} = \frac{(45.0~kg)(4.00~m)+(60.0~kg)(2.50~m)}{105.0~kg}$
$x_{cm} = 3.143~m$
The center of mass is now 3.143 meters from the left end of the canoe. Since the center of mass remained fixed, the canoe must have moved a distance of (3.143 m) - (1.857 m), which is 1.29 meters.
