Physics (10th Edition)

The two slide together at a speed of $3.51m/s$.
We have Ashley, with mass $M=71kg$ and $V=+2.7m/s$, and Miranda, with mass $m=58kg$ at $v=+4.5m/s$. After Miranda jumps into the tube, the system has mass $M+m=129kg$ and runs at velocity $V_f$, which needs to be found. Since friction is ignored, the total linear momentum is conserved. Therefore, $$M\vec{V}+m\vec{v}=(M+m)\vec{V}_f$$ $$\vec{V}_f=\frac{M\vec{V}+m\vec{v}}{M+m}=+3.51m/s$$ So the two slide together at a speed of $3.51m/s$.