The rates of throwing apples across the fence in both directions then would be the same:

=

=

The ratio of these standoff, or steady-state, concentrations, will tell us the relative agilities of the man and boy:

/ = /

This ratio of apples in the two yards when the stalemate is reached will be the same no matter what the starting conditions-whether all of the apples began in the boy's or the man's yard, or were shared between them at the beginning. The ratio of apples in the two yards at equilibrium also will be the same no matter how many apples were involved - a dozen or a thousand (as long as we can rule out fatigue).