2011 AMC 10A 第 15 题

Question

Roy 买了一辆新的电池汽油混合动力汽车。一次旅行中，汽车前

40

英里只使用电池，之后的路程只使用汽油，每英里耗油

0.02

加仑。整趟旅行平均每加仑行驶

55

英里。这趟旅行总长多少英里？

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?

140

240

440

640

840

设只用汽油行驶的距离为

x

。

Let

x

be the gasoline-only distance

每加仑英里数方程为

\frac{x+40}{0.02x}=55

。

The miles per gallon equation is

\frac{x+40}{0.02x}=55

设汽车只用汽油行驶的距离为

x

，则

\dfrac{40 + x}{0.02x} = 55\text{。}

交叉相乘并化简得

40 = 0.1x

x = 400\text{。}

因此旅程总长为

400 + 40 = 440

。

所以正确答案是 C。

Let

x

be the distance the car drove solely on gasoline. We have that

\dfrac{40 + x}{0.02x} = 55.

Cross-multiplying and simplifying gives

40 = 0.1x

x = 400.

The total length of the trip is then

400 + 40 = 440.

Thus, C is the correct answer.

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