Answer
The log moved a distance of 1.33 meters.
Work Step by Step
There is no external force acting on the system, so the location of the center of mass remains fixed.
We can find the center of mass when the two people are at opposite ends. Let Burt's position be the origin.
$x_{cm} = \frac{(20.0~kg)(1.5~m)+(40.0~kg)(3.0~m)}{90.0~kg}$
$x_{cm} = 1.667~m$
The center of mass is 1.667 meters from Burt.
We can find the center of mass when both people are at the same end. Let Burt's position be the origin in this new position.
$x_{cm} = \frac{(20.0~kg)(1.5~m)}{90.0~kg}$
$x_{cm} = 0.333~m$
The center of mass is 0.333 meters from Burt.
In the new position, the center of mass is 0.333 meters from Burt. However, the location of the center of mass remained fixed. Therefore, the log must have moved a distance of (1.667 m) - (0.333 m), which is 1.33 meters.
