Question

Yan 位于家和体育场之间。要到体育场，他可以直接走到体育场；也可以先走回家，再骑自行车到体育场。他骑车速度是步行速度的 $7$ 倍，且两种选择所需时间相同。Yan 到家的距离与到体育场的距离之比是多少？

Yan is somewhere between his home and the stadium. To get to the stadium he can walk directly to the stadium, or else he can walk home and then ride his bicycle to the stadium. He rides $7$ times as fast as he walks, and both choices require the same amount of time. What is the ratio of Yan's distance from his home to his distance from the stadium?

$\dfrac{2}{3}$

$\dfrac{3}{4}$

$\dfrac{4}{5}$

$\dfrac{5}{6}$

$\dfrac{6}{7}$

答案：B

知识点：路程、速度与时间比与比例

难度评级：1420

解答：

设 Yan 到家的距离和到体育场的距离分别为 $x$ 和 $y$ ，步行速度为 $w$ 。

直接步行到体育场需要 $\dfrac{y}{w}$ 。走回家再骑车需要 $\dfrac{x}{w} + \dfrac{x + y}{7w}$ 。

令二者相等，得 $7y = 8x + y$ ，所以 $8x = 6y$ ，从而 $\dfrac{x}{y} = \dfrac{3}{4}$ 。

所以正确答案是 B。

Let $x$ and $y$ be Yan's distances from home and from the stadium, and let $w$ be his walking speed.

Walking to the stadium takes $\dfrac{y}{w}.$ Walking home and biking takes $\dfrac{x}{w} + \dfrac{x + y}{7w}.$

Setting these equal gives $7y = 8x + y,$ so $8x = 6y$ and $\dfrac{x}{y} = \dfrac{3}{4}.$

Thus, the correct answer is B.

2007 AMC 10A 第 13 题

答案：B

难度评级：1420

解答：

其他年份的第 13 题