Achilles and the turtle

It is known that Achilles will not catch up with the turtle. But his brother Auchalles can do it. He even gave the turtle an 8-hour lead. Calculate how far from the start Auchalles will meet a turtle moving at an average speed of 70 m/h, if Auchalles walks slowly at a speed of 2.5 km/h

Correct result:

s =  0.5761 km

Solution:

$$\begin{gathered} v_1=2.5\text{ km/h } \\ {v}_2=70\mathrm{/}1000={\displaystyle \frac{7}{100}}=0.07\text{ km/h } \\ s=v_2\cdot (t+8)=0.5761\text{ km } \\ s=v_1\cdot t \\ s=0.07\cdot (t+8) \\ s=2.5\cdot t \\ s-0.07t=0.56 \\ s-2.5t=0 \\ s={\displaystyle \frac{140}{243}}\doteq 0.576132 \\ t={\displaystyle \frac{56}{243}}\doteq 0.230453 \end{gathered}$$

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Paradox

Achilles and the tortoise is an ancient paradox by which Zénón allegedly proved the impossibility of movement. Achilles - the fastest runner - never catches up with the turtle a bit ahead of him. The moment it reached the original place of the turtle, the turtle moved a little further. When Achilles runs this piece, the turtle is a little further again and so on to infinity.

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