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Suppose the trip was m miles. Because the first 70 miles did not require gas and the car consumes 1/40 gallons of gas per mile when it doesn’t run on its battery, during the trip (m-70)/40 gallons of gas were consumed.

54 = total miles/total gallons

So 54 = 40m/(m-70)

54(m-70) = 40m
14m = 54(70)
m = 54(5)=270
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Really good question, here's how I solved it.
Let total miles ran on gas = x. Then total gasoline used = 0.025x.
Now according to the formula, fuel efficiency = total distance / total fuel used i.e. 54 = (70+x) / 0.025x
54(0.025x) = 70+ x => 1.350x = 70+x
=> .350x = 70 => x = 70/.350 = 200. Hence, total distance = 70+200 = 270.
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