Answered by BobPursley following a repost.
They apparently want you to assume the marksman and gun recoil backwards together, as a rigid body with no force keeping them in place. That isn't really what happens, although it does apply to the center of mass of gun and marksman for a brief instant.
A marksman at rest fires a 4.00-kg gun that expels a bullet of mass 0.0140 kg with a velocity of 181 m/s. The marksman's mass is 81.0 kg. What is the marksman's velocity after firing the gun?
mc = 85kg
md = 0.0140
-(0.0140)(-181)/85
= .0298 m/s
2 answers
Thanks for nothing Bob