<image>The process depicted in the diagram shows Xiaoming going from home to the cafeteria for breakfast, then to the library to read the newspaper, and finally returning home. In this context:
$$x$$ represents time,
$$y$$ represents the distance Xiaoming is from home,
and Xiaoming's home, the cafeteria, and the library are all on the same straight line. 

$$(1)$$ How many minutes does it take Xiaoming to reach the farthest point from home? At this point, how far is he from home in $$km$$?
$$(2)$$ How far is the cafeteria from home in $$km$$? How many minutes does Xiaoming spend having breakfast in the cafeteria?
$$(3)$$ What is the average speed of Xiaoming from home to the cafeteria in $$km/min$$? What is the average speed of Xiaoming from the library back home in $$km/min$$?
$$(4)$$ When is Xiaoming 0.3 km from home? Write out the calculation process.