So here's an example of how it works:
Credit card 1: $5,000 at 12%
Credit card 2: $10,000 at 17%
Credit card 3: $15,000 at 15%
Under Ramsey's debt snowball, the underlying principle is that you pay off your debt balances with the smallest amounts first. Why? It's a psychological trick to keep you on track. You see that you're making progress. So in the example above you would pay credit card 1 off first, then 2, then 3, only in that order. This is counterintuitive to a mathematician or in this case an accountant.
Whoop-dee-fucking-doo! 1 month is nothing! Especially when you take into effect that under the accountant's method you are less likely to finish at all.
In case you can't tell, I'm in favor of the "debt snowball" rather than the conventional thinking. You are much more likely to succeed when you see progress, rather than having to see it all happen at the end. Have you ever tried to lose weight??
So focus on amounts, not interest rates. If you have a few credit cards with a $1,000 on each, then a car loan for $5,000, then another credit card for $10,000, then student loan for $30,000 and finally the mortgage for $150,000. Go after it in that order! Don't be afraid to mix and match. There are some specific exceptions to this rule given each person's unique situation, but it's a good rule of thumb to follow.