2016 MCM Problem A
A Hot Bath
A person fills a bathtub with hot water from a single faucet and settles into the bathtub to cleanse and relax.
一个人用一个水龙头让浴缸装满了热水，（然后？）睡进去来清洗和放松。

//那就先放到一定的程度，泡进去，然后边加水这样。

Unfortunately, the bathtub is not a spa-style tub with a secondary heating system and circulating jets, but rather a simple water containment vessel.
不幸的是，这个浴缸没有温泉热水模式，就是没有另外的加热系统和循环的喷嘴，而是个简单的水密闭容器。

After a while, the bath gets noticeably cooler, so the person adds a constant trickle of hot water from the faucet to reheat the bathing water.
不一会儿，这个水池明显的变冷了，所以这个人打开水龙头，加入了持续的细细的水，来加热这个浴缸里面的水。

The bathtub is designed in such a way that when the tub reaches its capacity, excess water escapes through an overflow drain.
这个浴缸设计成一种形式，当这个池子到达了它的容量，多余的水会通过一个溢出排水系统排出。

Develop a model of the temperature of the bathtub water in space and time to determine the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water.
设计一个浴缸里面的水温度关于空间和时间上的模型，去决定最好的策略，让这个人在浴缸里能够在不浪费太多的水的前提下，去尽量的靠近初始的温度。

Use your model to determine the extent to which your strategy depends upon the shape and volume of the tub, the shapeolume/temperature of the person in the bathtub, and the motions made by the person in the bathtub.
用你的模型去决定你的策略对以下因素的依赖程度（依赖关系）。

因素为：缸的形状和容量，这个浴缸里面的人的形状，体积，温度，还有这个人在浴缸里面的动作。

If the person used a bubble bath additive while initially filling the bathtub to assist in cleansing, how would this affect you r model’s results?
如果这个人在一开始装满这个浴缸的时候，就加入了泡泡添加剂去帮助清洗，这个会如何影响你的模型的结果呢？
In addition to the required one-page summary for your MCM submission, your report must include a one-page non-technical explanation for users of the bathtub that describes your strategy while explaining why it is so difficult to get an evenly maintained temperature throughout the bath water.
除了已经要求的一页的总结，你的报告必须含有一页的对浴缸使用者的非技术性的解释，去描述你的策略，同时解释为什么如此难以做到保持整个洗澡水的水温是均匀的。