AMC8 2019

AMC8 2019 · Q16

AMC8 2019 · Q16. It mainly tests Linear equations, Rates (speed).

Qiang drives $15$ miles at an average speed of $30$ miles per hour. How many additional miles will he have to drive at $55$ miles per hour to average $50$ miles per hour for the entire trip?

Qiang 以平均时速 30 英里/小时驾驶了 15 英里。要使整个行程的平均时速达到 50 英里/小时，他还需要以 55 英里/小时多驾驶多少英里？

(A) 45 45

(B) 62 62

(D) 110 110

(E) 135 135

Answer

Correct choice: (D)

正确答案：（D）

Solution

The only option that is easily divisible by $55$ is $110$, which gives 2 hours of travel. And, the formula is $\frac{15}{30} + \frac{110}{55} = \frac{5}{2}$. And, $\text{Average Speed}$ = $\frac{\text{Total Distance}}{\text{Total Time}}$. Thus, $\frac{125}{50} = \frac{5}{2}$. Both are equal and thus our answer is $\boxed{\textbf{(D)}\ 110}.$

唯一容易被 55 整除的选项是 110，这对应 2 小时的行驶时间。公式为 \frac{15}{30} + \frac{110}{55} = \frac{5}{2}。平均速度 = \frac{总距离}{总时间}。因此，\frac{125}{50} = \frac{5}{2}。两者相等，因此答案是 \boxed{\textbf{(D)}\ 110}。

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