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2007 AMC 10B Problem 3

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2007 AMC 10B Problem 3AMC 10 Step by Step
Name:                             Date: September 13, 2026
Ratios, Percents & Averages · difficulty 2 of 5 · about 2 min · position P1-10

A college student drove his compact car 120120 miles home for the weekend and averaged 3030 miles per gallon. On the return trip the student drove his parents' SUV and averaged only 2020 miles per gallon. What was the average gas mileage, in miles per gallon, for the round trip?

  1. A)

    2222

  2. B)

    2424

  3. C)

    2525

  4. D)

    2626

  5. E)

    2828

Answer

B

Key insight

Average mileage is total miles over total gallons: 240 miles on 4 + 6 = 10 gallons gives 24, not the naive average 25.

Solution

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

Trip home: 120120 miles at 3030 miles per gallon uses 120/30=4120/30 = 4 gallons.

Trip back: 120120 miles at 2020 miles per gallon uses 120/20=6120/20 = 6 gallons.

The round trip covers 240240 miles on 1010 gallons:
24010=24 miles per gallon.\frac{240}{10} = 24 \text{ miles per gallon}.

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

Why this works

When two rates apply over equal distances, the overall rate is the harmonic mean, which is always less than the ordinary average because more of the resource (gas, time) is spent on the slower or less efficient leg. Always go back to the definition: total output over total input.

The trap

Averaging 30 and 20 to get 25, which ignores that the less efficient car burns more gas over the same distance.

Common mistakes

  • Averaging 30 and 20 to get 25, which ignores that the less efficient car burns more gas over the same distance.
  • Dividing 120120 (one leg) by 1010 gallons (both legs) and getting 1212, or otherwise mixing one-way and round-trip figures.

Techniques

Set up the equation/formula and compute; no special trick needed