A man of mass

m$1=64\mathrm{.}5$ kg

is skating at

v$1=7\mathrm{.}65$ m$/$s

behind his wife of mass

m$2=51\mathrm{.}0$ kg$,$

who is skating at

v$2=3\mathrm{.}95$ m$/$s$.$

Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. $($b$)$ Is the collision best described as elastic, inelastic, or perfectly inelastic, why? Solve the momentum equation for vf$.($Use the following as necessary: m$1,$ v$1,$ m$2,$ v$2.$ Do not substitute numerical values; use variables only.$)$ Substituting values, obtain the numerical value for vf$,$ their speed after the collision.