A black boat is on shore A and a purple boat is on the opposite shore B of a lake. Each boat starts at the same time for the opposite shore.

The boats meet and pass each other 500 units from shore A. Each boat gets to the opposite shore and immediately starts a return journey. The two boats then meet and pass 300 units from shore B.

How long is the lake, and what is the ratio of speeds between the purple and black boats?