Problem 19 · 1986 AJHSME
Hard
Ratios, Rates & Proportions
miles-per-gallongas-used-only
At the beginning of a trip, the mileage odometer read 56,200 miles. The driver filled the gas tank with 6 gallons of gasoline. During the trip, the driver filled his tank again with 12 gallons of gasoline when the odometer read 56,560. At the end of the trip, the driver filled his tank again with 20 gallons of gasoline. The odometer read 57,060. To the nearest tenth, what was the car's average miles-per-gallon for the entire trip?
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Answer: D — 26.9.
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Hint 1 of 3
The numbers are designed to trip you up. MPG = miles ÷ gas *used*. The very first 6 gallons were poured in *before* any of the measured driving — so does that gas belong in 'gas used during the trip'?
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Hint 2 of 3
A refill replaces exactly the gas you just burned. So the gas used between the start and end odometer readings is the sum of the *later* fill-ups, not the first one.
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Hint 3 of 3
Miles = end odometer − start odometer; gas used = the two refills made during the trip.
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Approach: miles driven ÷ gas burned (the refills during the trip)
- First the easy part: miles driven = 57,060 − 56,200 = 860 miles.
- Now the trap. The opening 6 gallons just filled the tank at the start — that gas measures driving from *before* this trip, not during it. Every refill afterwards replaces exactly what was burned since, so the gas used over these 860 miles is 12 + 20 = 32 gallons.
- MPG = 860 ÷ 32 = 26.875 ≈ 26.9.
- Why exclude the first fill: 'miles per gallon' pairs the distance with the fuel that distance consumed. Including the initial top-off (giving 860⁄38 ≈ 22.6, choice B — the planted wrong answer) would mix in fuel for earlier miles. Match the gas to the miles it actually moved.
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