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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 equal x/50, and city gallons equal 2x/v, where v is the city rate. The whole-trip average is (x + 2x) ÷ (x/50 + 2x/v), and that equals 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, and 100 city miles use 4 gallons, so 150 miles on 5 gallons is 30 miles per gallon, matching the given trip average. So the answer is C.
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