AMC10 2005 A

AMC10 2005 A · Q7

AMC10 2005 A · Q7. It mainly tests Rates (speed).

Josh and Mike live 13 miles apart. Yesterday Josh started to ride his bicycle toward Mike’s house. A little later Mike started to ride his bicycle toward Josh’s house. When they met, Josh had ridden for twice the length of time as Mike and at four-fifths of Mike’s rate. How many miles had Mike ridden when they met?

Josh 和 Mike 相距 13 英里。昨天 Josh 开始骑自行车向 Mike 家骑去。稍后 Mike 开始骑自行车向 Josh 家骑去。他们相遇时，Josh 的骑行时间是 Mike 的两倍，且速度是 Mike 速度的四分之五。他们相遇时 Mike 骑了多少英里？

(A) 4 4

(B) 5 5

(D) 7 7

(E) 8 8

Answer

Correct choice: (B)

正确答案：（B）

Solution

Because (rate)(time) = (distance), the distance Josh rode was $(4/5)(2) = 8/5$ of the distance that Mike rode. Let $m$ be the number of miles that Mike had ridden when they met. Then the number of miles between their houses is $13 = m + (8/5)m = (13/5)m$. Thus $m = 5$.

因为 (rate)(time) = (distance)，Josh 骑的距离是 $(4/5)(2) = 8/5$ Mike 骑的距离。设 $m$ 是他们相遇时 Mike 骑的英里数。那么两家之间的距离是 $13 = m + (8/5)m = (13/5)m$。因此 $m = 5$。

Topics

AR.007 Rates (speed)