I think boat also change the velocity, due to this we assumed, the man does not apply force on BOAT A,
As we have
FC→A=0=ΔpAΔt⇒ΔpA=0⇒mA(vA+dvA)−(mA+mC)vA=0⇒dvA=mCmAvA.
So conservation of momentum equation is:
(mA+mC)vA+mBvB=mA(vA+dvA)+(mB+mC)(vB+dvB).