AMC10 2011 A

AMC10 2011 A · Q15

AMC10 2011 A · Q15. It mainly tests Linear equations, Rates (speed).

Roy bought a new battery-gasoline hybrid car. On a trip the car ran exclusively on its battery for the first 40 miles, then ran exclusively on gasoline for the rest of the trip, using gasoline at a rate of 0.02 gallons per mile. On the whole trip he averaged 55 miles per gallon. How long was the trip in miles?

Roy买了一辆新的电池-汽油混合动力车。在一次旅行中，该车前40英里完全用电池行驶，其余路程完全用汽油，汽油消耗率为每英里0.02加仑。整个行程平均55英里每加仑。行程总长多少英里？

(A) 140 140

(B) 240 240

(D) 640 640

(E) 840 840

Answer

Correct choice: (C)

正确答案：（C）

Solution

Answer (C): Let $x$ be the number of miles driven exclusively on gasoline. Then the total number of miles traveled is $x+40$, and the amount of gas used is $0.02x$ gallons. Therefore the average number of miles per gallon is $$ \frac{x+40}{0.02x}=55. $$ Solving results in $x=400$, so the total number of miles traveled is $440$.

答案（C）：设 $x$ 为完全使用汽油行驶的英里数。则总行驶英里数为 $x+40$，使用的汽油量为 $0.02x$ 加仑。因此，每加仑的平均行驶英里数为 $$ \frac{x+40}{0.02x}=55。 $$ 解得 $x=400$，所以总行驶英里数为 $440$。

Topics