A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 540-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 6 meters per second. Let t represent the number of seconds that have elapsed since the start gun was fired. Write an expression in terms of t that represents the hare's distance from the starting line (in meters). Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters). Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare. Who finishes the race first?

To know who finishes first, we can find where both meet (the hare overtakes the tortoise). This happens when C = 0. The time of this event is t = 540/3 = 180.

How far are the runners at t = 180 ? At this time A = 9*180 = 1620 > 1200. Then the winner is the tortoise.

francocanacari francocanacari · Answer 2 · 2021-10-26T14:03:26+02:00

The Tortoise will finish the race in 110 seconds, while the Hare will do it in 133.33 seconds.

Since a tortoise and a hare are competing in a 1200-meter race, and the hare decides to let the tortoise have a 540-meter head start, and the hare begins running at a constant speed of 9 meters per second and the tortoise begins crawling at a constant speed of 6 meters per second, to determine who finishes the race first, the following linear equations must be performed:

Tortoise =
(1200 - 540) - 6X = 0
660 - 6X = 0
660 = 6X
660/6 = X
110 = X

Hare =
1200 - 9X = 0
1200 = 9X
1200/9 = X
133.33 = X

Therefore, the Tortoise will finish the race in 110 seconds, while the Hare will do it in 133.33 seconds.

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