2011 AMC 10A Problems/Problem 15

Problem 15

Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of gallons per mile. On the whole trip he averaged miles per gallon. How long was the trip in miles?

Solution 1

We know that . Let be the distance in miles the car traveled during the time it ran on gasoline, then the amount of gas used is . The total distance traveled is , so we get . Solving this equation, we get , so the total distance is .

Solution 2

Let be the length of the trip in miles. Roy used no gasoline for the 40 first miles, then used 0.02 gallons of gasoline per mile on the remaining miles, for a total of gallons. Hence, his average mileage was Multiplying both sides by , we get Then , so . The answer is .

Solution 3 (Answer choices)

Since Roy had 0 gasoline usage during the first 40 miles, and we know his usage is 0.02 gallons per mile after that, we can look at all 5 individual answers and simply run them through.

If Roy drove (A) 140 miles would mean he spent 140 - 40 = 100 miles on gasoline, so he used 100 * 0.02 = 2 gallons. = 70 miles per gallon which does not equal 55, so (A) is incorrect. Similarly, (B) 240 gives: 240 - 40 = 200 miles on gasoline, 200 * 0.02 gallons = 4 gallons, = 60 m/g which does not equal 55.

Plugging in (C) 440, we get: 440 - 40 = 400, 400 * 0.02 = 8, = 55 miles per gallon, so answer choice

Video Solution

https://youtu.be/HQmkIPpuIEc

~savannahsolver

See Also

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