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A tortoise and a hare are competing in a 2000-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 8 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.

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Toshu25

The distance covered by the hare and the tortoise in t seconds are 8t and 5t respectively. (Simple Speed-Distance-Time relation)

The tortoise gets a 510m headstart so at t=0 is 1490m.

The functions representing the distance of both of them from the finish line is,

F(x)=2000-8t,. for hare

G(x)=1490-5t,. for tortoise