Setting up a subdomain in apache

So, I have two web applications on one server. I have a main one which is served when the regular domain is used, but I want a subdomain to point to the other app.

I have set up virtual hosts in the way that I have determined they should be with what I have found in google searches, but it still doesn't work. The subdomain just serves up the main app. Here is the contents of my config file.

<VirtualHost *:80>
        ServerName www.luketimoth.me
        DocumentRoot /var/www/luketimothy/public

       <Directory /var/www/luketimothy/public>
          <IfModule mod_rewrite.c>
          Options -MultiViews
          RewriteEngine On
          RewriteCond %{REQUEST_FILENAME} !-f
         RewriteRule ^ index.php [L]
         </IfModule>
       </Directory>
</VirtualHost>

<VirtualHost *:80>
        ServerName www.luketimoth.me
        DocumentRoot /var/www/shattered-plays/public
        ServerAlias shattered.luketimoth.me

        <Directory /var/www/shattered-plays/public>
          PassengerEnabled on
        </Directory>
</VirtualHost>

As far as I am aware (with my beginner/rudimentary knowledge of Apache) this should do what I am expecting it to... but it's not. What am I doing wrong?

Output of httpd -S

httpd: apr_sockaddr_info_get() failed for LMTServe
httpd: Could not reliably determine the server's fully qualified domain name, using 127.0.0.1 for ServerName
[Sat May 17 16:42:02 2014] [warn] _default_ VirtualHost overlap on port 80, the first has precedence
VirtualHost configuration:
wildcard NameVirtualHosts and _default_ servers:
*:80                   www.luketimoth.me (/etc/httpd/conf/httpd.conf:1017)
*:80                   www.luketimoth.me (/etc/httpd/conf/httpd.conf:1031)
Syntax OK

EDIT:

I have changed the virtual host to use the desired subdomain as the ServerName, but I am still seeing the same problem.

<VirtualHost *:80>
        ServerName www.luketimoth.me
        DocumentRoot /var/www/luketimothy/public

       <Directory /var/www/luketimothy/public>
          <IfModule mod_rewrite.c>
          Options -MultiViews
          RewriteEngine On
          RewriteCond %{REQUEST_FILENAME} !-f
         RewriteRule ^ index.php [L]
         </IfModule>
       </Directory>
</VirtualHost>

<VirtualHost *:80>
        ServerName shattered.luketimoth.me
        DocumentRoot /var/www/shattered-plays/public

        <Directory /var/www/shattered-plays/public>
          PassengerEnabled on
        </Directory>
</VirtualHost>

httpd: apr_sockaddr_info_get() failed for LMTServe
httpd: Could not reliably determine the server's fully qualified domain name, using 127.0.0.1 for ServerName
[Sun May 18 10:15:24 2014] [warn] _default_ VirtualHost overlap on port 80, the first has precedence
VirtualHost configuration:
wildcard NameVirtualHosts and _default_ servers:
*:80                   www.luketimoth.me (/etc/httpd/conf/httpd.conf:1017)
*:80                   shattered.luketimoth.me (/etc/httpd/conf/httpd.conf:1031)
Syntax OK