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

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

游客2024-08-09  12
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间才能灌满？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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