The Hare and tortoise are back for a rematch, a 1-mile-long race. Five minutes i

Question

The Hare and tortoise are back for a rematch, a 1-mile-long race. Five minutes into the race, the arrogant hare figures that he can take a 40-minute nap and still win easily because it takes him only 10 min to cover 1 mile and because he thinks that the toroise's top speed is 1 mile/ hr. Littlee does the hare know: the tortoise has been working out; and, as he passes the napping hare, he is able to increase his speed from 1 mile/hr to 5/3 mile/hr. When the hare wakes up, he sees the tortoise way ahead. With what minimum speed must the hare now run in order to win the race?

Explanation / Answer

let both start from x=0, t=0 , after five min hare will travel 1/2 mile, and start taking nape

tortoise start with 1mile/hr , after 30 min. tortoise cross the hare and now start moving with 5/3 mile / hr.

time wiil be taken by tortoise to complete the race = (1/2)/5/3 = 3/10 hrs = 18min.

now hare sleeps till t=45 min

time left for hare after hare wake up before race completed = 18- 15 = 3min

distance left for hare to travel = 1/2 mile,

min. speed needed= (1/2)/ (3/60) = 10 mile/hr

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