You are trying to fill a bath with both taps on, but have accidentally left out

游客2024-08-09  10

问题 You are trying to fill a bath with both taps on, but have accidentally left out the plug. Normally the hot water tap takes 8 minutes to fill the bath and the cold water tap takes 10 minutes. However, the water empties out through the plug hole in 5 minutes. How long will it take for the bath to fill?

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答案 40 minutes

解析 题干意思是:你打开浴缸里的两个龙头,却不小心把浴缸的塞子给漏掉了。通常热水龙头需要8分钟来充满浴缸,冷水龙头需要10分钟。然而,水通过塞子孔在5分钟内流出。请问洗澡水要多长时问才能灌满?由于浴缸的体积不变,因此不管是热水还是冷水,灌满后的水的量是一样的。设浴缸容量为m,x为三管一起开的充满水的时间,热水充满浴缸要8分钟,所以每分钟充满m/8,同理冷水每分钟充满m/10,而放水管每分钟放水m/5,故可列方程(m/8+m/10-m/5)mx=m,解得n=40,即需40分钟。由此可知本题答案。
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