Does Windows use the fastest drive for the page file?

Solution 1:

Well if they didn't change anything about page files from XP it should use the least active drive. So whatever drive has more usage it will pick the other drive.

The paging file on the less frequently accessed partition is used most frequently because it is on a partition that is least busy. - https://support.microsoft.com/en-us/kb/314482

Also a page file is a fixed size if set by hand. So it getting bigger would not be an issue. Also having a page file on your SSD could potentially wear down your SSD quicker.

Solution 2:

The best way would be to disable the page file on the HDD, and only enable the page file on the SSD. You probably gain nothing from having two separate page files anyway, especially from one that is on a HDD while you have a much faster SSD available.

Just uncheck "Automatically manage paging file size for all drives" in the Virtual Memory setting dialog, then set the settings manually.