AMC8 2006

AMC8 2006 · Q13

AMC8 2006 · Q13. It mainly tests Rates (speed).

Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba and Marquette. At what time in the morning do they meet?

Cassie 在上午8:30 从 Escanaba 出发骑车前往 Marquette，匀速12英里/小时。Brian 在上午9:00 从 Marquette 出发骑车前往 Escanaba，匀速16英里/小时。他们在 Escanaba 和 Marquette 之间相同的62英里路线上骑行。他们上午几点相遇？

(A) 10:00 10:00

(B) 10:15 10:15

(D) 11:00 11:00

(E) 11:30 11:30

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) Between 8:30 and 9:00 AM Cassie travels 6 miles. At 9:00 Cassie and Brian are only 56 miles apart. After 9:00, because they are both biking towards each other, the distance between them decreases at the rate of $12+16=28$ miles per hour. At that rate, it will take them $\frac{56}{28}=2$ hours to meet. So they will meet at 11:00 AM.

（D）在上午 8:30 到 9:00 之间，Cassie 行驶了 6 英里。到 9:00 时，Cassie 和 Brian 相距只有 56 英里。9:00 之后，因为他们都朝着彼此骑行，两人之间的距离以每小时 $12+16=28$ 英里的速度减少。按这个速度，他们需要 $\frac{56}{28}=2$ 小时才能相遇。所以他们会在上午 11:00 相遇。

Topics

AR.007 Rates (speed)