2013 AMC 12B 第 4 题

Question

Ray 的车平均每加仑汽油行驶

40

英里，Tom 的车平均每加仑汽油行驶

10

英里。Ray 和 Tom 各自行驶相同的英里数。两辆车合起来的每加仑英里数是多少？

Ray’s car averages

40

miles per gallon of gasoline, and Tom’s car averages

10

miles per gallon of gasoline. Ray and Tom each drive the same number of miles. What is the cars’ combined rate of miles per gallon of gasoline?

10

16

25

30

40

合并油耗是总英里数除以总加仑数，不是两个油耗率的普通平均。

Combined mileage is total miles divided by total gallons, not the average of the two rates

若每人行驶

D

英里，耗油分别为

\dfrac{D}{40}

与

\dfrac{D}{10}

加仑。

If each drives

D

miles, the gallons used are

\dfrac{D}{40}

and

\dfrac{D}{10}

若每人行驶

D

英里，两人共行驶

2D

英里，耗油量为

\dfrac{D}{40}+\dfrac{D}{10} = \dfrac{D}{8}

加仑。因此合并油耗率为

\dfrac{2D}{\frac{D}{8}} = 16

英里每加仑。正确答案是 B。

If each drives

D

miles, together they cover

2D

miles using

\dfrac{D}{40}+\dfrac{D}{10} = \dfrac{D}{8}

gallons. The combined rate is

\dfrac{2D}{\frac{D}{8}} = 16

miles per gallon. Thus, the correct answer is B.

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