AMC 8 2020 Problem 11

AMC8 2020 年第 11 题

行程问题★★★☆☆

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 出发去距学校 6 英里的沙滩。Maya 决定骑车去，而 Naomi 坐公交车去。下图展示了他们的行程，显示了时间和所走路程的关系。那么 Naomi 和 Maya 的平均速度之差是多少英里每小时？

A.6
B.12
C.18
D.20
E.24

正确答案 · Correct Answer

解析 · Solution

Solution 1

Naomi travels 6 miles in a time of 10 minutes, which is equivalent to

\dfrac{1}{6}

of an hour. Since

\displaystyle \text{speed} = \frac{\text{distance}}{\text{time}}

, her speed is

\displaystyle \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 = 24. Naomi's speed of 6 miles in 10 minutes is equivalent to

6 \cdot 6 = 36

miles per hour, while Maya's speed of 6 miles in 30 minutes (i.e. half an hour) is equivalent to

6 \cdot 2 = 12

miles per hour. The difference is consequently 36-12=24.

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