AMC12 2013 B

AMC12 2013 B · Q4

AMC12 2013 B · Q4. It mainly tests Rates (speed).

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?

雷的车平均每加仑汽油行驶40英里，汤姆的车平均每加仑汽油行驶10英里。雷和汤姆各开相同的里程。两车的综合每加仑汽油里程数是多少？

(A) 10 10

(B) 16 16

(D) 30 30

(E) 40 40

Answer

Correct choice: (B)

正确答案：（B）

Solution

Answer (B): Let $D$ equal the distance traveled by each car. Then Ray’s car uses $\frac{D}{40}$ gallons of gasoline and Tom’s car uses $\frac{D}{10}$ gallons of gasoline. The cars combined miles per gallon of gasoline is \[ \frac{2D}{\left(\frac{D}{40}+\frac{D}{10}\right)}=16. \]

答案（B）：设 $D$ 表示每辆车行驶的距离。那么 Ray 的车耗油 $\frac{D}{40}$ 加仑，Tom 的车耗油 $\frac{D}{10}$ 加仑。两车合计的每加仑行驶里程为 \[ \frac{2D}{\left(\frac{D}{40}+\frac{D}{10}\right)}=16。 \]

Topics

AR.007 Rates (speed)