题目
Dick takes twice as long as Jane to run any given distance.
Starting at the same moment, Dick and Jane run towards each other from opposite ends of the schoolyard, a total distance of x, at their respective constant rates until they meet
Quantity A
The fraction of the total distance x that is covered by Jane
选项
C.The two quantities are equal.
D.The relationship cannot be determined from the information given.
解析
已知:
跑相同的距离,Dick 所用时间是 Jane 的**两倍**。
也就是说,**Jane 的速度是 Dick 的两倍**。
Dick 每跑 1 米,Jane 就跑 2 米。
已知:
两人同时从操场两端出发,相向而跑,总距离为 \(x\),直到相遇。
这是**相遇问题(closing gap 问题)**。
Dick 每向 Jane 跑 1 米,Jane 就向 Dick 跑 2 米。
也就是说,每缩短 3 单位距离:
- Dick 跑 1 单位
- Jane 跑 2 单位
总距离是 \(x\),两人合起来一共跑了 \(x\)。
所以:
- Dick 跑了 \(\dfrac{1}{3}x\)
- Jane 跑了 \(\dfrac{2}{3}x\)
因此:
- Quantity A:\(\dfrac{2}{3}x\)
- Quantity B:\(\dfrac{2}{3}x\)
**答案:C(两者相等)**