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 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.

Answer:The required function is [tex]f(t)=1090-5t[/tex]Step-by-step explanation:Consider the provided information.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. The tortoise begins crawling at a constant speed of 5 meters per second.The distance covered by tortoise in t second is:[tex]Distance=speed \times time[/tex][tex]Distance=5\times t=5t[/tex]We need to 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.[tex]f(t)=1600-510-5t[/tex][tex]f(t)=1090-5t[/tex]Hence, the required function is [tex]f(t)=1090-5t[/tex]