00:01
And hello, calculus student.
00:03
We're looking at chapter 12, section 4, problem 35.
00:07
This is a story about achilles running a race against a tortoise.
00:13
So achilles is going to be running at 10 meters per second.
00:16
The tortoise is a little bit slower at 1 meter per second.
00:20
But the tortoise has a 10 meter head start.
00:23
So the question becomes how long for achilles to catch the tortoise.
00:28
So we're going to do this two different methods.
00:30
So part a using a geometric series idea.
00:34
So we'll start by saying that let's keep track of the distance that achilles needs to run, or i should say actually the time that achilles needs to run in order to catch up to the tortoise.
00:52
So we can start by saying, okay, during that first 10 meters that the tortoise has a head start, that will take achilles one second since he's going to be running at 10 meters per second.
01:08
So we can say he's going to run for one second.
01:13
While he ran for one second, the tortoise will have run one more meter since he's running at one meter per second.
01:22
So achilles then has to take that one meter, and he's running at 10 meters per second.
01:29
So it's going to take him one tenth of a second to make up that time.
01:34
Meanwhile, the tortoise is traveled during that one -tenth of a second at one meter per second.
01:43
So he's at one -tenth of a meter.
01:49
And to catch up, achilles is going to be running at his speed of 10 meters per second.
01:56
And this pattern is just going to keep going.
01:59
So will be the tortoise then during that short time is going to run.
02:07
Distance of 1 -100th of a meter.
02:11
And to catch up, running at 10 meters per second, and this pattern will just keep going.
02:19
So we can simplify this down and say that achilles is going to run for one second, then 1 tenth of a second, then 1 -100th of a second, then 1 -1 ,000th of a second, dot, dot, dot...