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Ancient mathematical prose
The "one hundred steps" mentioned in the poem title and the original title are not the 100 steps we are taking at will now. In ancient times, "step" was a unit of length, 1 step =5 feet, which is about 1.67 meters now. We must pay attention to this when solving this problem. As for "good walkers" and "bad walkers", it is easier to understand, that is, two walkers who walk fast and slow.

If this question is expressed in popular words, it can be

There are two people, A can walk and B can't. At the same time, A took 100 steps, while B could only take 60 steps. Now that B has left 100 step, A has just started to catch up with B. Q: How many steps does A have to take to catch up with B?

In the Nine Chapters of Arithmetic, an interesting solution to this problem is given. The problem-solving "skills" and answers in the book are:

"Those who do good take a hundred steps, those who do evil take sixty steps, and the remaining forty steps are the law; It is true that good people take a hundred steps and bad people take a hundred steps. This is as good as the law. " "Answer: 250 steps. "

The word "Fa" in calligraphy is the ancient name of "divisor" and "Shi" is the ancient name of "dividend". "Reality is like a step of the law", that is, divide the obtained "reality (dividend)" by "law (divisor)" and you will get the number of steps required by the topic.

This solution of the ancients, if expressed in the present formula, can be

100-60 = 40 ………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

100× 100 = 10000 ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

10000÷40=250 (step size) ... If the steps are combined, it is

100×100 ÷ (100-60) =10000 ÷ 40 = 250 (step size)

A: A good walker can catch up with a poor walker in 250 steps.

Why can this be worked out?

According to the basic quantitative relationship of "tracking problem"

Distance ÷ (speed difference) = catch-up time

People who do good need time to catch up with those who do bad things.

100÷( 100-60)=2.5 (unit time)

And in these 2.5 "unit time", the number of steps a good walker needs to take is

100×2.5=250 (step size)

This is the answer to this question.

If it is listed as a comprehensive formula, it can

100×[ 100÷( 100-60)]