Wednesday, November 30, 2016

mathematics - A walk of 3000 meters, but one foot has moved more, how so?


My math teacher has struck again.


Here's his newest riddle:




Today I went for a normal walk of 3000 meters.
One of my feet had to move exactly 3000 meters.
However, the second foot moved 3100 meters.



Can you justify how did that happen?


Edit:


I am not sure how this question has been selected as too broad.
It clearly only has a tag and the correct answer has been given and accepted in a fast way. If people decided to answer it using it doesn't mean that the question is too broad, it means that posters just want to get the "funny" comments and a "+1".



Answer




Based on @TwoBitOperation's answer



and assuming his feet are 25 centimeters apart, if he walks $n$ circles with a radius of $r$ meters in a single direction, one foot walks $2 \pi r n$ meters, and the other one $2 \pi (r + 0.25) n$. The difference, $\pi n / 2$ is 100 meters, so $n = 200 / \pi \approx 63.6$. The value of $r$ is then determined from $2 \pi r n = 3000$ so $2 r = 15$ and $r$ = 7.5 meters.



Whether these



63.6 turns around e.g. a fountain or pond with a 15m diameter constitute a "normal walk" remains an open discussion.



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