SOLUTION: 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 o

Question 1028432: 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???
Answer by ikleyn(52798) (Show Source): You can put this solution on YOUR website!
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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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Let "u" be the Achilles race speed, in .
Then the tortoise race speed is  , 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,  should be less than the tortoise time :

 < ,   or

5000 < (5000-h)*10,   or

5000 < 50000 - 10h   --->   10h < 450000   --->   h <  = 4500 m.

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