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 530-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 5 meters per second. a. 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. f(t) = b. Solve f(t) = 0 for t. t = c. Define a function g to represent the hare's distance from the finish line (in meters) in terms of the number of seconds t since the start of the race. g(t) = d. Solve g(t) = 0 for t. t = e. Who won the race? Select an answer

Transcript

00:01 So the theme in this problem is basically distance equals rate times time.

00:06 The difference, though, is that if you're from the finish line, that you want to start out with a negative distance.

00:17 Or maybe you want to do, how about this? i'll just give you the answer.

00:22 For the first one, is f of t is we are 2 ,000 meters, but.

00:31 We're moving closer to the finish line.

00:34 So you want to subtract off the, let's see, five meters per second.

00:39 So five times t.

00:40 And you can double check that this is the right answer because if you plug in one second in for t, you'd be 1995 away.

00:51 And it should make sense.

00:53 So if you're asked to solve for letter b, you just set this equal to zero by the time they finish.

01:01 And what i would do is subtract, or sorry, add 5t to the right side and divide by 5.

01:08 And i believe this answer would be t would equal 400.

01:14 You double check 2 ,000 divided by 5.

01:18 So it would take 400 seconds.

01:23 I don't know if you need to convert that, but that's the units that we're looking for.

01:28 So the next one is a little bit trickier because this thing, it doesn't say when the hair started moving.

01:43 It just said that gave the first one a 530 meter head start.

01:54 So for, i guess, several seconds, i guess the hair is not moving at all.

02:06 And when does the hair start moving is after, so i don't know if you're allowed to make a piecewise function in this, but for a while, the hair is not moving from zero seconds all the way until what i would do is figure out when the tortoise gets to 530.

02:30 So 2 ,000 minus 5t is equal to 530...

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