AMC8 2014

AMC8 2014 · Q17

AMC8 2014 · Q17. It mainly tests Fractions, Rates (speed).

George walks $1$ mile to school. He leaves home at the same time each day, walks at a steady speed of $3$ miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first $\frac{1}{2}$ mile at a speed of only $2$ miles per hour. At how many miles per hour must George run the last $\frac{1}{2}$ mile in order to arrive just as school begins today?

乔治步行1英里去学校。他每天同一时间离开家，以3英里每小时的恒定速度走路，恰好在学校开始时到达。今天他被宜人的天气分心了，前半英里只以每小时2英里的速度走。为了今天能恰好在学校开始时到达，乔治必须以多少英里每小时的速度跑完最后的半英里？

(A) 4 4

(B) 6 6

(D) 10 10

(E) 12 12

Answer

Correct choice: (B)

正确答案：（B）

Solution

Note that on a normal day, it takes him $1/3$ hour to get to school. However, today it took $\frac{1/2 \text{ mile}}{2 \text{ mph}}=1/4$ hour to walk the first $1/2$ mile. That means that he has $1/3 -1/4 = 1/12$ hours left to get to school, and $1/2$ mile left to go. Therefore, his speed must be $\frac{1/2 \text{ mile}}{1/12 \text { hour}}=\boxed{6 \text{ mph}}$, so $\boxed{\text{(B) }6}$ is the answer.

注意正常情况下，他去学校需要花费1/3小时。然而，今天他用$\frac{\frac{1}{2} \text{英里}}{2 \text{英里每小时}}= \frac{1}{4}$小时走完了前半英里。这意味着他剩下的时间是 $ \frac{1}{3} - \frac{1}{4} = \frac{1}{12} $ 小时，剩下的距离是半英里。因此，他的速度必须是 $\frac{\frac{1}{2} \text{英里}}{\frac{1}{12} \text{小时}} = \boxed{6 \text{英里每小时}}$，所以答案是 $\boxed{\text{(B) }6}$。

Topics