AMC10 2018 B

AMC10 2018 B · Q2

AMC10 2018 B · Q2. It mainly tests Linear equations, Rates (speed).

Sam drove 96 miles in 90 minutes. His average speed during the first 30 minutes was 60 mph (miles per hour), and his average speed during the second 30 minutes was 65 mph. What was his average speed, in mph, during the last 30 minutes?

Sam在90分钟内开车96英里。他前30分钟的平均速度是60 mph（英里每小时），第二30分钟的平均速度是65 mph。最后30分钟的平均速度是多少mph？

(A) 64 64

(B) 65 65

(D) 67 67

(E) 68 68

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Sam covered $\frac{1}{2}\cdot 60 = 30$ miles during the first 30 minutes and $\frac{1}{2}\cdot 65 = 32.5$ miles during the second 30 minutes, so he needed to cover $96 - 30 - 32.5 = 33.5$ miles during the last 30 minutes. Thus his average speed during the last 30 minutes was $\dfrac{33.5\ \text{miles}}{\frac{1}{2}\ \text{hour}} = 67\ \text{mph}.$

答案（D）：Sam 在前 30 分钟行驶了 $\frac{1}{2}\cdot 60 = 30$ 英里，在第二个 30 分钟行驶了 $\frac{1}{2}\cdot 65 = 32.5$ 英里，因此他在最后 30 分钟需要行驶 $96 - 30 - 32.5 = 33.5$ 英里。于是他在最后 30 分钟的平均速度为 $\dfrac{33.5\ \text{英里}}{\frac{1}{2}\ \text{小时}} = 67\ \text{英里/小时}.$

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