AMC8 2010

AMC8 2010 · Q8

AMC8 2010 · Q8. It mainly tests Rates (speed).

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 view 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?

艾米莉骑自行车在一条长直路上行驶时，发现前方半英里处有埃默森在同方向滑旱冰。她超过他后，通过后视镜能看到他，直到他落后她半英里。艾米莉以恒定速度12英里/小时骑行，埃默森以恒定速度8英里/小时滑行。艾米莉能看到埃默森多少分钟？

(A) 6 6

(B) 8 8

(D) 15 15

(E) 16 16

Answer

Correct choice: (D)

正确答案：（D）

Solution

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 \[\frac12 \ \text{mile} \cdot \frac{1\ \text{hour}}{4\ \text{miles}} = \frac18\ \text{hour}\] 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 \[2 \cdot \frac18 \ \text{hour} \cdot \frac{60\ \text{minutes}}{1\ \text{hour}} = \boxed{\textbf{(D)}\ 15}\ \text{minutes}\]

因为他们都朝同一方向运动，艾米莉相对于埃默森的速度是 $12-8=4$ 英里/小时。现在可以看作埃默森不动，艾米莉以 $4$ 英里/小时骑行。她骑行到他身边的时间是 \[\frac12 \ \text{mile} \cdot \frac{1\ \text{hour}}{4\ \text{miles}} = \frac18\ \text{hour}\] 然后同样时间骑行到领先他半英里。总时间是 \[2 \cdot \frac18 \ \text{hour} \cdot \frac{60\ \text{minutes}}{1\ \text{hour}} = \boxed{\textbf{(D)}\ 15}\ \text{minutes}\]

Topics

AR.007 Rates (speed)