Problem:

I'm currently reading a little about DNA replication, and have come accross the following statement;
Replication starts from a fixed point and is bi-directional ... In Eukaryotes, there are multiple replication forks, each progressing in a bi-directional fashion.

If there is a single, long strand of DNA in a Eukaryotic cell, I see potential problems with this:

These forks involve opening up a section of double-stranded DNA, and each strand becoming a double strand in a newly synthesised piece of DNA. At some point, before any single fork has become two new double-stranded molecules, another fork could 'collide' with this, causing it to attempt to replicate the non-finished section.

Question: How can one replication fork meet another without either exponentially increasing the number of strands being replicated?
Also, on a more general level, I would be quite interested to know the actual benefit of this, when, typically, only a single copy of the double-stranded molecule needs making.

Please justify.