Does not make since how they will ever reach the same amount because the .60 is clearly always going to be more no matter how many miles they are at.

Hey Angela, the simplest way to do this problem is setting both sides equal to each other. You'll have 55 + .1x = .6x. You can do this with virtually any "when will plan A be equal to plan B" type of problem. Now, as we have our equation, let's solve for x; 55 = .6x - .1x => 55 = .5x. Next, we divide 55/.5 = 110 = x. Therefore, at 110 miles, the plans will be the same.

Another example of this would be say plan A is $45 down and $0.10 per mile, plan B is $65 down and $.05 a mile. Which plan would be better if you were driving 50 miles.

Setting this up in the same way, we get 45 + .10x = 65 + .05x. Combine like terms, and we get .05x = 20. Dividing, we'll get x = 400 miles is where they're equal, with the Plan A better for short periods and plan B better for longer periods (lower slope).