Question

A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 550-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? Select an answer: Hare or Tortoise.

          A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 550-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? Select an answer: Hare or Tortoise.

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Added by Carmen Z.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Gregory Higby

11/01/2022

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Step 1: Write an expression in terms of t that represents the hare's distance from the starting line (in meters). Show more…

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A tortoise and a hare are competing in a 1200-meter race. The arrogant hare decides to let the tortoise have a 550-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? Select an answer: Hare or Tortoise.

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Transcript

00:01 I think there's a couple ways you can think about this problem.

00:04 Like you can start with the hair.

00:06 I'll just write h right here.

00:10 Now write it a little bit higher because its rate is higher, faster, because he's going nine meters per second, if my memory is correct, versus the tortoise that i'll use t for.

00:27 But he starts a lot higher at time zero, starting five.

00:32 550 meters away, you know, in front of the hair.

00:40 But its rate is lower because he's only going six meters per second.

00:46 But if i are coming up with an equation for the tortoise over time, it would be 6t plus 550.

00:56 Now, if you're not used to my notation here and function notation, you might just write it as y equals but i'm going to leave it like that same thing with h of t but it because they the hair started at the line it's just going to be nine t so if you want to see how a equation write an expression that represents a number of meters of tortoises ahead uh what i would do so maybe i'll just do this one's y equals is take the tortoises equation and then subtract off the hair's equation.

01:38 So your final answer would look like this and they give 3t plus 550 typo there.

01:50 So i think i'm supposed to have all of these answers.

01:52 But the whole thought process is, is the tortoise still ahead of the hair when they finish the race, which is 1 ,200 meters from the start? so that's all i would do is set the equation equal to 1 ,200.

02:09 Subtract the 550 over.

02:15 So we get negative 3t is equal to, what's that, 1 ,200 minus 550, which is 650, and then divide by negative 3.

02:43 Oh, that's not what i want...

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