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my bud came up w/ this chart tho. for the distance the tortoise traveled is this:
xn* = 1 + xn-1 (6+3t)/(3+3t)
time x L L-x
t 3 + 3t
0 1 3 2
1 3 6 3
2 5.5 9 3.5
3 8.333333333 12 3.666666667
4 11.41666667 15 3.583333333
5 14.7 18 3.3
6 18.15 21 2.85
7 21.74285714 24 2.257142857
8 25.46071429 27 1.539285714
9 29.28968254 30 0.71031746
10 33.21865079 33 -0.218650794
xn is a previous distance x the tortoise walked, and says he does make it using old x over old L multiplied by new L
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