AMC8 2015

AMC8 2015 · Q17

AMC8 2015 · Q17. It mainly tests Linear equations, Rates (speed).

Jeremy's father drives him to school in rush hour traffic in 20 minutes. One day there is no traffic, so his father can drive him 18 miles per hour faster and gets him to school in 12 minutes. How far in miles is it to school?

杰里米的父亲在高峰期交通中开车送他上学用20分钟。有一天没有交通，所以父亲可以比平时快18英里每小时，并在12分钟内送他到学校。到学校有多远（英里）？

(A) 4 4

(B) 6 6

(D) 9 9

(E) 12 12

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Because the new time is $\frac{12}{20}=\frac{3}{5}$ of the original time, the new speed must be $\frac{5}{3}=1\frac{2}{3}$ of the original speed. Then the additional $18$ miles per hour must be $\frac{2}{3}$ of the original speed, which is then $27$ mph. In $20$ minutes, Jeremy’s father travels $\frac{1}{3}\cdot27=9$ miles.

答案（D）：因为新的时间是原来时间的 $\frac{12}{20}=\frac{3}{5}$，所以新的速度必须是原来速度的 $\frac{5}{3}=1\frac{2}{3}$ 倍。于是增加的每小时 $18$ 英里应当等于原来速度的 $\frac{2}{3}$，因此原来的速度是 $27$ 英里/小时。在 $20$ 分钟内，Jeremy 的父亲行驶了 $\frac{1}{3}\cdot27=9$ 英里。

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