The time could take hundreds of years, if not thousands, or millions.

https://stackoverflow.com/questions/11807869/how-to-crack-aes-128-encryption-used-in-winrar

The idea is that the encryption does not actually store the password that any brute force can find out.
Decryption thru brute force will not work in reasonable time.

There was an article I found many days ago about how encrypted .rar file is way much more secure than encrypted .zip file, I tried to find it but can't.

Edit:
The article explained well why a good password-protected .rar file cannot be cracked/decrypted by brute force or any software program.
But of course it would be great if I can have Mike B's email to send him a strong password-protected .rar file to prove me wrong.