A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 580-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. 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) = 1200-5t + 580 Incorrect Solve f (t) = 0 for t. t = Incorrect 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) = Incorrect Solve g (t) = 0 for t. t = Incorrect Who won the race? Incorrect

Step-by-step explanation:

The total distance to be covered in the race is 1200 meters.

Distance = speed * time

The arrogant hare decides to let the tortoise have a 580-meter head start. The tortoise begins crawling at a constant speed of 5 meters per second when the start gun is fired.

If t represents the number of seconds since the start of the race, then the distance covered by the tortoise is 580 + 5t

Therefore, the function f, used to represent the tortoise's distance from the finish line (in meters) would be

f (t) = 1200 - (580 + 5t)

f (t) = 1200 - 580 - 5t

f (t) = 620 - 5t

For f (t) = 0,

620 - 5t = 0

5t = 620

t = 125 seconds

When the start gun is fired the hare begins running at a constant speed of 9 meters per second. The 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 would be

g (t) = 1200 - 9t

If g (t) = 0, then

1200 - 9t = 0

9t = 1200

t = 1200/9 = 133.33 seconds

The tortoise won the race.