In what way do the parasympathetic and the sympathetic work together

They work in opposite direction in order to maintain organism's homeostasis.

Explanation:

Parasympathetic and sympathetic nervous systems are part of the autonomic nervous system which controls unconscious actions within the body.

The parasympathetic system is  system that works while orgnism is at rest, so it is responsible for stimulation of "rest-and-digest" stimulation. On the other hand sympathetic system is active during the stress situations and it is said that it stimulates activities associated with the fight-or-flight response.

So, for example both of those systems are involved in the control of heart rate: parasympathetic decreases heart rate, while sympathetic system increases contraction and heart rate.

a motor homunculus represents a map of brain areas dedicated to motor processing for different anatomical divisions of the body.

homunculus represents the importance of various parts of your body as seen by your brain. as a result, they take up a lot of brain space. although the cortical homunculus is a curiosity, penfield's work in mapping the brain's relationship to the body was invaluable.

it also supports my hypothesis. if you rest first you can squeeze the clothespin more times. from the data i collected the average of the eight people concluded exercise makes your muscles more fatigued and less able to squeeze the clothespin compared to resting before squeezing.