2007 AMC 10B Problem 3

"Miles per gallon" for the whole trip means total miles divided by total gallons. So find how much gas each half used.

1. Going home: $120$ miles at $30$ miles for each gallon. That takes
$$120 \div 30 = 4 \text{ gallons}.$$
2. Coming back: $120$ miles at $20$ miles for each gallon. That takes
$$120 \div 20 = 6 \text{ gallons}.$$
3. Whole trip: $120 + 120 = 240$ miles, and $4 + 6 = 10$ gallons.
4. Average mileage:
$$240 \div 10 = 24 \text{ miles per gallon}.$$

The answer is $\boxed{\textbf{(B)}\ 24}$.

The two halves cover the same distance, but not the same amount of gas. The SUV burns more gallons, so its poor mileage counts for more in the total, and the answer lands below the simple average of $25$. Whenever you average rates, go back to the meaning: total of one thing divided by total of the other.

Average mileage means total distance divided by total fuel, so find the fuel used on each leg.

Trip home: $120$ miles at $30$ miles per gallon uses $120/30 = 4$ gallons.

Trip back: $120$ miles at $20$ miles per gallon uses $120/20 = 6$ gallons.

The round trip covers $240$ miles on $10$ gallons:
$$\frac{240}{10} = 24 \text{ miles per gallon}.$$

The answer is $\boxed{\textbf{(B)}\ 24}$.