[old] Achilles and the Tortoise [old] Achilles and the Tortoise
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In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

– as recounted by Aristotle, Physics VI:9, 239b15

"Achilles and the tortoise" is one of the famous Zeno's paradoxes. Nikola wants to check the validity of this paradox and for this purpose he constructed two robots: Achilleborg (A1 -- fast agile prototype) and Tortoimenator (T2 -- heavy slow cyborg).

A1 is faster than T2, so it has... seconds head start on A1. For seconds T2 will move metres. So A1 must first reach the point which T2 has already reached. But T2 is moving and next step for A1 is to reach the next point and so on to . The paradox is correct in theory, but in practice A1 easily outruns T2. Hm... maybe we can calculate when A1 will catch up with T2.

You are given A1 and T2’s speed in m/s as well as the length of the advantage T2 has in seconds. Try to count the time when A1 will catch up with T2 (count from the T2’s start). The result should be given in seconds with precious ±10-8.

Input: Three arguments. The speed of A1 and T2, and the advantage as integers.

Output: The time when A1 will catch up with T2 (count from the T2’s start) as an integer or float.


chase(6, 3, 2) == 4
chase(10, 1, 10) == 11.11111111

How it is used: Let's go back to school for a moment and remember the basic math principles. Sometimes simple arithmetic allows us to easily resolve philosophical paradoxes.

t2_speed < a1_speed < 343
0 < advantage ≤ 60

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