Question 1028432
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Achilles is asked to race against the tortoise in 5000m run, with the condition that the tortoise is given a head start. Achilles knows that his velocity is 10 times the velocity of tortoise. What can the head start be at most in order that Achilles would win the race???
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<pre>
Let "u" be the Achilles race speed, in {{{m/s}}}.
Then the tortoise race speed is {{{u/10}}} {{{m/s}}}, according to the condition.

Let "h" will be the value of the tortoise head start, in meters.
Then the tortoise should cover only 5000-h meters.

To win, Achilles time, {{{5000/u}}} should be less than the tortoise time {{{(5000-h)/((u/10)))}}}:

{{{5000/u}}} < {{{(5000-h)/((u/10)))}}},   or

5000 < (5000-h)*10,   or

5000 < 50000 - 10h   --->   10h < 450000   --->   h < {{{450000/10}}} = 4500 m.
</pre>