Host multiple Rack apps on one server with multiple ports (using Apache and Passenger)

I've search online and been reading documentation for Apache, Passenger, Rack, etc, but have yet to find a solution to my problem.

I have several Rack (ruby)-based apps, located in

/home/web/sites/app1
/home/web/sites/app2
/home/web/sites/app3

app1 is a Sintra app, app2 is Padrino and app3 is Rails.

I would like to run these apps under different ports (assuming server IP is 50.60.70.101):

50.60.70.101:4567 -> app1
50.60.70.101:3000 -> app2
50.60.70.101:80   -> app3

What is the correct way to configure Apache's virtual host file to achieve this?

I have 3 files in /etc/apache2/sites-available/ with this type of configuration (with changed IPs):

<VirtualHost *:4567>
    RackEnv         production

    DocumentRoot    /home/web/sites/app1/public
    <Directory      /home/web/sites/app1/public>
        Order   allow,deny
        Allow   from all
        Options -MultiViews
        #AllowOverride All
    </Directory>
</VirtualHost>

But I cannot access app1 at 50.60.70.101:4567 (app3 does work on port 80, though).