河宽

River Length

专题: Brainteaser / 脑筋急转弯
难度: L2
来源: QuantQuestion

题目详情

你在一条河里，河宽与水流速度未知。

若你保持不游泳（随水漂），6 秒到达对岸。
若你以 3 英尺/秒的速度顺流游，4 秒到达对岸。

问：河的宽度是多少（英尺）？

You are in a river with an unknown length and current speed. If you remain stationary (not swimming) in the river, it takes you $6$ seconds to reach the opposite bank. If you swim downstream at a speed of $3$ feet per second, it takes you $4$ seconds to reach the opposite bank. What is the length of the river (in feet)?

解析

设水流速度为 $v$ （英尺/秒），河宽为 $\ell$ 。

随水漂： $\ell=6v$ 。

顺流游：有效速度 $v+3$ ，所以 $\ell=4(v+3)$ 。

联立：

6v=4(v+3)\Rightarrow 2v=12\Rightarrow v=6.

因此

\ell=6\cdot 6=36.

Original Explanation

Denote $v$ to be the velocity of the river and $l$ to be the length. From the first part of the question we know that:

l = 6v

Furthermore, we have that

l = 4(v+3)

from the question, where we swim downstream. Using these equations, we have that

6v = 4(v+3) \iff 2v = 12 \iff v = 6

Therefore, we have that

l = 6 \cdot 6 = 36