TrackTime is tested on Joomla! 2.5; if you're using a previous version, please upgrade as soon as possible. We strongly suggest you to always use the latest Joomla! version, since it patches all the known bugs.
To avoid any kind of problems, your PHP version should be at least 5.3.
However, you can use an older version (5.2), but you could incurr in some issues. Since version 5.2 is dated 2006, you really should find an hosting with an updated version of PHP.