AMC 8 2010 Problem 8

AMC8 2010 年第 8 题

行程问题★★☆☆☆

As Emily is riding her bicycle on a long straight road, she spots Emerson skating in the same direction 1/2 mile in front of her. After she passes him, she can see him in her rear mirror until he is 1/2 mile behind her. Emily rides at a constant rate of 12 miles per hour, and Emerson skates at a constant rate of 8 miles per hour. For how many minutes can Emily see Emerson?

当 Emily 在一条长直公路上骑着她的自行车时，她发现前方 1/2 英里处 Emerson 正朝着同方向滑冰。当她经过他以后，她可以一直在后视镜里看到他，直到他在她后方 1/2 英里处。 Emily 骑车的速度是 12 英里每小时，而 Emerson 滑冰的速度是 8 英里每小时。那么 Emily 在多少分钟内可以一直看到 Emerson？

A.6
B.8
C.12
D.15
E.16

正确答案 · Correct Answer

解析 · Solution

Solution 1

Because they are both moving in the same direction, Emily is riding relative to Emerson 12-8=4 mph. Now we can look at it as if Emerson is not moving at all [on his skateboard] and Emily is riding at 4 mph. It takes her

\displaystyle \frac12 \ \text{mile} \cdot \frac{1\ \text{hour}}{4\ \text{miles}} = \frac18\ \text{hour}

to ride the 1/2 mile to reach him, and then the same amount of time to be 1/2 mile ahead of him. This totals to

\displaystyle 2 \cdot \frac18 \ \text{hour} \cdot \frac{60\ \text{minutes}}{1\ \text{hour}} = 15\ \text{minutes}

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