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On a certain workday, a delivery van traveled twice as many miles on city streets as on the highway. The van averaged 50 miles per gallon of fuel on the highway and a constant lower rate on city streets, and it averaged exactly 30 miles per gallon over the entire workday. What was the van's fuel rate, in miles per gallon, on city streets?
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Correct answer
C
This is a blended fuel rate, a weighted average where the weight is gallons consumed, not miles driven. The trip-wide miles per gallon equals total miles divided by total gallons, so the two leg-rates must be combined by gallons, not by the more visible mileage figures.
Let the highway distance be x miles, so the city distance is 2x miles. Highway gallons = x/50, and city gallons = 2x/v, where v is the city rate. The whole-trip average is (x + 2x) divided by (x/50 + 2x/v) = 30. The x cancels, leaving 3 ÷ (1/50 + 2/v) = 30, so 1/50 + 2/v = 1/10. Then 2/v = 1/10 − 1/50 = 5/50 − 1/50 = 4/50 = 2/25, giving v = 25. Sanity check: 50 highway miles use 1 gallon, 100 city miles use 4 gallons, so 150 miles on 5 gallons is 30 miles per gallon. So the answer is C.
Among the traps: A averages the two rates directly, (50 + v)/2 = 30, but rates do not combine by a plain average when the legs differ. B is the dominant trap, weighting the rates by the 1-to-2 miles ratio, (1×50 + 2×v)/3 = 30, or treating that mileage ratio as a fuel ratio; in reality more city miles at a lower rate means city gallons dominate, pulling the weight far past a mileage split. D restates the overall trip average 30 as the city rate. E keeps the correct total of 5 gallons over 150 miles but wrongly splits the fuel evenly (2.5 gallons per leg), when the lower-rate city leg actually consumes 4 of the 5 gallons.
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