As my high school physics and chemistry teachers used to say, 'Use those Units!' Let me try to add a little more math to the already lucid discussion by Shiloh and rgx. I love numbers!

You ought to calculate it this way:

1 mile over x gallons = 30 miles per gallon (1/x = 30, so x = 1/30)
1 mile over y gallons = 60 miles per gallon (1/y = 60, so y = 1/60)

You need to calculate what two miles over x+y gallons is, so you take
2 miles over (1/30 gallons + 1/60 gallons) = 2/(3/60) = 2/(1/20) = 2*20 = 40 mpg.

Your original math, in words, has the numerators and denominators reversed, and it's like you're trying to add fractions by saying

a/x + a/y = a/(x+y), which just isn't so. [side note: in fact, a/x + a/y = a(y+x)/xy]

You were thinking of this equation:
a/x +b/x = (a+b)/x, but you have a direct proportion instead of an indirect one, which you can tell by checking the units (measuring in inverse gallons instead of gallons, for instance).

If this helps you understand it, I'm glad. Try chugging through it with different numbers if you like.

1 mile at 2 mpg + 1 mile at 200 mpg- Could it get you 101 mpg?
2/(1/2 + 1/200)= 3.96 mpg.

Consider the logic. You wasted a half gallon going that first mile. No matter how crazily efficient your second mile is, you still wasted that half gallon already, and you can't get it back. So think about it- after the second mile, even if you've used barely a drop more than half a gallon, the best you could be at is 2 miles for half a gallon= 4 mpg. Twice the distance, so twice the mpg. Not 'halfway to whatever other mpg you were travelling at for the second mile,' because that could be a lot more.

One little hit has huge repercussions on the average because we're talking about inverses. Your whole 'only a quarter mile of acceleration' can still be a huge hit if you use a ton of gas to do it, no matter what your mpg is before or after that quarter mile.

Good luck!