AMC8 2020

AMC8 2020 · Q11

AMC8 2020 · Q11. It mainly tests Averages (mean), Rates (speed).

After school, Maya and Naomi headed to the beach, $6$ miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?

放学后，Maya 和 Naomi 前往 6 英里外的海滩。Maya 决定骑自行车，而 Naomi 坐公交车。下图显示了她们的旅程，标明了时间和行驶距离。Naomi 和 Maya 的平均速度差多少英里每小时？

(A) 6 6

(B) 12 12

(D) 20 20

(E) 24 24

Answer

Correct choice: (E)

正确答案：（E）

Solution

Naomi travels $6$ miles in a time of $10$ minutes, which is equivalent to $\dfrac{1}{6}$ of an hour. Since $\text{speed} = \frac{\text{distance}}{\text{time}}$, her speed is $\frac{6}{\left(\frac{1}{6}\right)} = 36$ mph. By a similar calculation, Maya's speed is $12$ mph, so the answer is $36-12 = \boxed{\textbf{(E) }24}$.

Naomi 在 10 分钟内行驶 6 英里，相当于 $\frac{1}{6}$ 小时。由于 $\text{speed} = \frac{\text{distance}}{\text{time}}$，她的速度是 $\frac{6}{\left(\frac{1}{6}\right)} = 36$ mph。类似计算，Maya 的速度是 12 mph，因此答案是 $36-12 = \boxed{\textbf{(E) }24}$。

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