A tortoise and a hare are competing in a 1600-meter race. The arrogant hare decides to let the tortoise have a 510-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.

b. Solve f (t) = 0for 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.

d. Solve g (t) = 0 for t

e. Who won the race?

(a) f (t) = 1090-5t

(b) f (0) = 1090metres

(c) g (t) = 1600-9t

(d) g (0) = 1600metres

(e) The Hare

Step-by-step explanation:

Total Distance = 1600 metres

(a) The tortoise has a 510m headstart and a speed of 5m/s

Distance=Speed X Time

Distance at 5m/s = 5t

Total Distance covered by the tortoise at any time t = 510+5t

Therefore, The tortoise's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race is given as:

f (t) = 1600 - (510+5t)

f (t) = 1090-5t

(b) f (0) = 1090 - (5X0)

=1090metres

(c) The hare has a speed of 9m/s

Distance=Speed X Time

Distance at 9m/s = 9t

Total Distance covered by the hare at any time t = 9t

Therefore, The hare's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race is given as:

g (t) = 1600-9t

(d)

g (0) = 1600 - (9X0) = 1600metres

(e) The race is finished when the distance from the finish line=0

For the Tortoise

f (t) = 1090-5t=0

1090=5t

t=218seconds

For the Hare

g (t) = 1600-9t=0

9t=1600

t=177.8seconds

The hare takes a shorter time to reach the finish line so he won the race.