Olmec's Public works

Water Systems 

A water system consisted of a buried network of stone troughs.
The long U-shaped rectangular blocks of basalt were laid end to end and covered with capstones. 
Aqueducts were used to provide drinking water to the different areas of the settlement.

Road Systems 

They built paved roads between different communities. In building the roads they established trade with other native groups in Central  America. The roads link each communities,  which resulted in a long network of ideas and new technologies to spread.

Pyramids 

The Olmecs built large pyramid like structures resembling a volcano. The reason that they built the large pyramid is to gather all the people into one area to worship the Gods and Goddesses. 

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 Chavin's Public works

The rugged terrain on which the Chavin lived, imposed arid coastal valleys that demanded irrigation. The Irrigation projects were enormous and involved miles of canals and ditches that required constant maintenance and construction. 
In the highlands, irrigation and terracing increased the food supply in the regions where the amount of arable land was limited. Populations concentrated in the fertile valleys, but were separated from each other by steep mountains. Trade and communication were difficult. It took large and well-organized projects to build roads, bridges, and agricultural terraces. The result       benefit the cities, but also required hard labor to be accomplished.