两人割草协作需要多久

Lawn Teamwork

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

题目详情

有两台割草机：Rabbit 单独割完一块草坪需要 1 小时，Turtle 单独割完需要 1 小时 15 分钟。

若两人一起割，割完一块草坪需要多少分钟？

There are two lawnmowers: Mr. Rabbit can mow a lawn in $1$ hour, Mr. Turtle needs $1$ hour and $15$ minutes. If they work together, how long does it take to mow one lawn (in minutes)?

解析

换算成每分钟工作率：

Rabbit： $\frac{1}{60}$ 块/分钟。
Turtle： $\frac{1}{75}$ 块/分钟。

合做率： $\frac{1}{60}+\frac{1}{75}=\frac{3}{100}$ 块/分钟。

设用时 $x$ 分钟，则 $\frac{3}{100}x=1\Rightarrow x=\frac{100}{3}$ 分钟。

Original Explanation

Given the information we have, we can solve for the rate at which both men mow a lawn per minute. Mr. Rabbit mows $\frac{1}{60}$ of a lawn per minute. Mr. Turtle mows $\frac{1}{75}$ of a lawn per minute. We can use $\text{rate}\cdot \text{time}=\text{work}$ done to solve for how long it takes. Let $x$ be the number of minutes it takes for both of them to do one lawn. $\left(\frac{1}{60} + \frac{1}{75}\right) \cdot x = 1$ lawn. Solving for $x$ , we get $\frac{100}{3}$ minutes.