A tortoise and a hare are competing in a 2000-meter race....

A tortoise and a hare are competing in a 2000-meter race. The arrogant hare decides to let the tortoise have a 520-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. Let t represent the number of seconds that have elapsed since the start gun was fired. a. Write an expression in terms of t that represents the hare's distance from the starting line (in meters). b. Write an expression in terms of t that represents the tortoise's distance from the starting line (in meters). c. Write an expression in terms of t that represents the number of meters the tortoise is ahead of the hare. d. Who finishes the race first?

Transcript

00:01 All right, let's think about a classic tortoise and hair race.

00:08 And who would win if the hair gave the tortoise a head start? so first, a few parameters, okay? the race itself is 2 ,000 meters.

00:22 The tortoise is going to get a 520 meter head start.

00:28 Okay.

00:32 So they get 520 meter head start and and they will be moving at five meters per second.

00:46 The hair has to start at the start line.

00:50 So no head start, obviously.

00:53 But then they're going to, they actually move faster because they're a hair faster than a horse.

00:58 So they remove at 8 meters a second.

01:02 So a couple questions to kind of get us started with all this.

01:05 The first one, just in terms of the tortoise in the hair, how would you write an expression for each of these? if we think about seconds in terms of the variable t for time, then each of these expressions are actually pretty easy.

01:21 For the tortoise, it would be 520 meters, so 520 plus 5t, because for every second that they start moving, they're going to go five more meters.

01:40 So 520 meters plus 5t.

01:42 For the hair, it's even more basic.

01:45 There's no head start, so zero meters.

01:48 And then just 8t.

01:50 For every second that goes by in this race, the hair is going to move 8 meters.

01:58 Now, when we think about the two together, wanted to write an expression to talk about the difference between these two.

02:09 We have to remember that the tortoise again is, you know, 520 meters ahead of the hair and moving at 5 meters per second.

02:21 But the hair is actually, you know, catching up.

02:28 And so they're running faster than the tortoise.

02:32 So we're actually taking away, you know, like the overall distance that the tortoise is ahead by eight meters a second...

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