Okay, so we have a problem here. One car leaves a given point, travelling north at thirty miles per hour. So let's draw a picture. So here's her point. One car leaves going thirty miles per hour. Then another car leaves the same point in tramples the west at forty miles per hour. And then we want to know what rate is the distance between the two cars changing at the instant when the cars have traveled to ours. So if the second car is out here in the first cars out here, here's the distance between them. Okay, So call it s And this is why I'LL say this is Axel wise. The distance that the first cars traveled North X is the distance that the second cars traveled traveling west, as is the distance between them. And so the relationship between ex twine s is, of course, western and northern perpendicular. So we have the part that I'm going to tear my ex career plus life squared is s squared. And, of course, thirty and forty are the rates of change of, uh, X and y said d x d t It's party the variety his thirty and So if we differentiate this with respect to TV A to X t X T plus two I divided team Nichols to S t s t t. Ok, And so what we need, I guess we have the extra weight density divided tur looking for D s tt We need X and y and s well, it says after two hours. Okay, so after two hours, So after two hours? Well, ex so that this second car has been traveling forty miles per hour. So it's gone eighty miles. Why? Has been traveling thirty miles for two hours, said sixty miles. And then if we come up here in just two eighty squared plus sixty squared is s squared Well, you do eighty square plus sixty squared. You've been and gets, uh, see ten thousand insolence for ten thousand one hundred. So s is one hundred. This is one hundred miles. That's nice. So then we have two times eighty times forty plus two times sixty. That's thirty equals two times, one hundred times. Well, we're looking for OK, And so everything has to everything has two zeros, So in forty, that's gonna give us one hundred times dividing my hundred and see what a real actors were left with AIDS times for plus six times. Three Nichols D s Dean team. And what is that? Well, this is thirty two was eighteen. So, fifteen, it is? Yes, into that's course miles per hour. Okay, so that was a party and part of being okay. So now we suppose that the second car, the one traveling west left one hour later than the first car. Well, everything is the same. So we still have this relationship. So this relationship here relating the race have changed. The race of change is still the same. So we still have X dx DT and divided by two. Because every term as a factor to s to t t. But what's different now? Well, now, after a cease after two hours, at what rate is the distance between the two cars changing An incident of the second car has travelled one hour. Well, now, instead of ex being eighty now, X is just going to be forty. Because when why has traveled for two hours, ex waited an hour, sit in trouble, anything anywhere and then traveled forty miles. So now X is eighty and why is still so excess forty? And why's sixty? So that means s changes. So we have. So what is s we know? Forty squared plus sixty squared now is s squared. It's part B. So then what is s well s is going to be about seventy two point one Now if we put everything in, we have forty times eighty plus a sixty Sturdy eagle seventy two point one one. Yes, Titi. And you just saw his calculator yesterday. T is about forty seven point one five miles per hour.