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

Quantity B

选项

A.

Quantity A is greater.

B.

Quantity B is greater.

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)**
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