Cart 1 of mass \(m\) and Cart 2 of mass \(2m\) are held at rest on a horizontal, frictionless track with a compressed ideal spring of negligible mass between them, as shown. At time \(t = 0\), the carts are released and push apart. The spring remains in contact with both carts until it reaches its uncompressed equilibrium length at time \(t = t_1\), at which point it detaches from both carts. During the interval \(0 \le t \le t_1\), Cart 1 travels a distance \(\Delta x_1\) and Cart 2 travels a distance \(\Delta x_2\). Which of the following correctly compares \(\Delta x_1\) to \(\Delta x_2\) and describes the motion of the center of mass of the two-cart system during this interval?