From where energy is gained or given?

Question

for example suppose we have in a linear smooth surface and 2 persons A and B equal masses. A pushes the B so B gains a velocity $u$ and A gains velocity $-u$ but both have same kinetic energy. my question is the energy that A and B have is came from the chemical energy of body of A who pushed?

Answer 1

Yes, the physical interpretation of a muscle action is adenosine triphosphate (ATP) being turned into adenosine diphosphate (ADP) in the right location of an array of proteins such that the energy released can be turned into a force between body parts, which usually turns into motion. (Exceptions in such cases as standing over a 4-foot wrecking ball and trying to lift it - forces are exerted, but nothing moves except except your sweat.)

Answer 2

If person A does the pushing then person A does the work at the expense of chemical energy stored in person A.
It is no different to person A pushing a rock instead of person B.