The length of time/amount of rings before a call can no longer be answered is a carrier-controlled feature. Adding a new ringtone will not change this.
This is not something you can control yourself. You can contact your mobile provider to increase the amount of time before your call goes to voicemail.
I'm right behind you in age but my phone is on me most of the time. I believe you can change the length of the rings on certain phones and with certain carriers.
It doesn't go by the number of rings but by seconds. I think 30 seconds is the longest ring time which is about 6 rings. Try calling your carrier to see if you can change it as @Mujibar said.
On some carriers, you can change the length of your ring time by dialing **61*101**XX#, with the XX being the number of seconds you want the the ringtime to be. So, if you want a 60 second ring time, you would dial **61*101**60#. If this doesn't work, your carrier should be able to do it for you
