We are spying on a train manufacturer’s collection of top-secret futuristic trains to determine some facts about how these high-speed trains are powered. We see from a posted sign that each train is composed of cars all of the same length. We are able to measure the front car of each train, and we find that the length of the cars differ slightly from train to train. Next, the manufacturer decides to test-drive the trains through a tunnel. Before test-driving each train, the total amount of energy powering the train is announced, which is slightly different for each train. It is also announced that all the trains travel at precisely the same speed. Upon each train being driven through the tunnel, we are able to count how many cars of the train exit the tunnel every 30 seconds, which of course is different for each train since they differ from each other in car length, but travel at the same speed. We find that, in comparing the trains, there is correspondence between their differences in total energy, and the difference in how many cars exit the tunnel every 30 seconds.(adsbygoogle = window.adsbygoogle || []).push({});

Since we could get no more information than this, the question to which we want an answer is simple. Is the total amount of energy powering the trains, which is slightly different for each train, necessarily a function of each train’s total length? If so, why? Or if not, why not?

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# I A logical problem for math whizzes

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