<image> An engineering project is jointly completed by Team A and Team B. First, Team A works alone for $$3$$ days, and the remaining work is completed by Team A and Team B together. The progress of the project satisfies the function relationship shown in the figure:
$$(1)$$ Find the analytic expression for part $$②$$ of the graph and calculate the total number of days required to complete the project;
$$(2)$$ The total payment for the project is $$80,000$$ yuan. If the wages are distributed according to the proportion of the work completed, how much should Team A receive?