We can express the rate at which the old man throws apples by

=

The rate is measured in apples per second across the fence, and is the concentration of apples on the man's side of the fence in apples per square foot of ground. The rate constant, , has units of square feet per second:





The value of expresses the agility of the old man, and his speed in covering the territory on his side of the fence.

The rate at which the boy throws apples back across the fence is given by

=

in which is the concentration of apples in the boy's yard, and is the rate constant, or agility constant, which tells how fast the boy gets around on his side of the fence, in square feet per second. Since we have assumed that the boy is livelier than the man, is greater than .