The hare and tortoise are back for a rematch, a 1 mile long race. Five minutes i
ID: 1327514 • Letter: T
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 30 min nap and still win easily because it takes him only 10 min to cover 1 mile and because he thinks that the tortoise's top speed is 1mi/h. Little 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/h to 5/3 mi/h. 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
Speed of hare = 1 mile / 10 minute
Distance covered by hare before nap = 5 * 1/10 = 0.5 mile
Intial speed of tortoise = 1 mi/h
Time taken by tortoise to cover 0.5 ml = 0.5/1 = 0.5 hr = 30 minutes
further distance covered by tortoise in the time hare is sleeping (now with speed 5/3 mi/h) = (5/60) hr * (5/3) mi/h = 25/180 mile
Distance remaining to be covered by tortoise = 0.5 - 25/180 = 0.361 mile
time need to cover this distance by tortoise = 0.361 *60 *3 /5 = 13 minutes
So the minimum speed at which hare has to run = 0.5* 60 / 13 = 2.31 mi/h
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.