SOLUTION: A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 530-meter head start. When the start gun is fired the hare begins run

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Question 1122643: A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 530-meter head start. When the start gun is fired the hare begins running at a constant speed of 9 meters per second and the tortoise begins crawling at a constant speed of 5 meters per second.
a. Define a function f to represent the tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.
f(t)=
b. solve f(t)=0 for t
t=
c. Define a function g to represent the hare's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race.
g(t)=
d. solve g(t)=0 for t
t=
e. who won the race
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Tortoise has to go 670 m
Does so at 5 m/sec os it will take 670/5=or 135 seconds to finish.
Distance from finish line is g(t)=670-5t for any time t.
For the hare, the distance from the finish is g(t)=1200-9t, for any time t
It will take the hare 1200/9 or 133.3 seconds to finish and the hare will win.
They meet at t where both equations are equal
670-5t=1200-9t
4t=530
t=132.5 seconds, at which time the rabbit is 1200-9(132.5)=7.5 m from the end and the tortoise is 670-5t=7.5 m from the end.