You will be out of luck. Apple gives up its are one you or one And aren't you by the corresponding average rate of our when puts, todo wants us to find different variants or different confirmations given the distance is equal to 80 on the AC tree are able to that's called 80 miles and 48 MPH. So for our own or she problem, it asks us to ultra very clear. Verify that are two is equal to 20 are one over R one minus 20. So it's by copying down our corresponding of equations that are two is equal 20 arm one over R one months 20. Okay, so, um, we know our one is D over t one and R two over t two. Oh, and Leslie d equals 80 articles. 40. Okay, so let's start by plugging teat and to our, um ah rate equation so are equal. Oh, well, first we need to isolate t. I guess are in this case Penis multiple by both sides. Divide both sides by our one for our anti plugging this into our arbitrate enough r is equal to well to over cheap one plus t two post aren't that will be over by deep over our over our bust meat over a far too about sequel to Perlis. Multiply both sides by the denominator of the right hand that I d over. But there are if people t d anarchy wanted Bisley are to to confirm our verification So that are they have or for tea. What it I slipped the look tiny Are you first to t d um yes or he over arm and bring here. We want to multiply both sides by art by nominator on the left hand side by both sides by the barrier on the hands so that would give us both are are on over are what from here Let's factor out the B and do not move, are I? And this gives us, um, looking anything are 40. So it's started what's multiplied and he talked denominator by our one for five farm on that is arm or and we could double by a little bit biting both in the murder and the nominee to when you are one over it. One over is equal to Archie. Sounds pretty familiar. I think this is our final four Archie Boles, 20 are one over. Our one month 20 Archie goals are one over our rent one minus 20 so that it's verified. Okay, so that's the first portion of our problem from now. We need to don't want to find our now we want to find our awesome told me. So let's put this into graph. Oh, so, um, just yeah, this little icon side is not only but why. So it's called that part. All right, Well, the variable on the right hand side is only excellence, but that just so it's in a form where kind of more used to ah, we don't the zeros or singular zero of our right hand side would be here When the numerator is equal to zero, we know the left hand side will be both as big girl. I'm gonna go. Are one cannot equal 20 is That would mean we're dividing. So that would be a nascent tote on as our one approaches infinity, Immuno are a few would equal 20 he could of life is like in and even see their budget money. So these are a few ass. And that's what will the graph look politic as well. No, um it's gonna cross through. That's two points. And it can't touch other look, something this key. And as R approaches infinity, it would be positive number with something like that. And we want to know what our assets on the money and Botham our correspondents you rates. That kind of just tells us my other great only well 20 MPH Where? Okay, the, uh oops. So far, Because basically would be impossible. So if try to plug it in? No, our goal to, um, to over t one plus two. Um, and we substituted in are to algebraic right or R two and R one ultra Brickley and from there and found a 20 in the denominator evident algebraic substitution is it's possible to do it isolating either r two or r one because both of these terms are basically symmetrical. That makes sense. So, um, it tells us neither are one. Nor aren't you? Well, 20 mission. Um, but that's just kind of just showing entre Brickley Oh, you won't find the third portion of although it's part seat. It asks us to verify Then, when arching was greater than art one or the speaker attorney would be greater than it's going. Um, that over drinks. Oh, the going speed with the between. Um, wait. Yeah. When the speeder training with greater than the speed going So are to be group within our one. Oh, Rachel. Uh huh. We are one. Okay, so when le going speed is greater than the returning speed. So I wrote it down wrong. Um, then the going speed would be between 20 and 40 MPH. She's even, and we chose up. So that means we're basically solving inequality already here. I want our Once, he and earlier we found the algebraic equivalent of our chew. So it's like that in the 20 are one. It's our man. 20 are one over R one minus 20. From here, we can move everything to one side and creative function than inequality. So in this case, I think I'm just gonna multiply. Both sides by the nominee are are in length. It wasn't funny. Are are ones finest are one. Money are ones with a very one sided, which gives us are ones. One of our 1.2. Its body is greater than throw from here. Let's all or one just so It's a little bit more comfortable with Paul as it's What's you X squared minus 40 clacks on. Then he walked, um, at City zero. Our easy Barone's let me off like you just quote X. That would give us X experts for me, Chelsea zeros of our functions are gonna throw on a horny look at the inequality from above. We have this same asking photos before because our one cannot equal 20 are one is able to x a strict theater that look Arab or zero that are also boat is gonna 20 okay on as FX Negative, Bennett He won't be a negative times a negative, which would give us positive. It is odd. Multiplicity time change as X approaches. But affinity, it would be a positive. So that would bust like that. Want to own when? After Brexit is going to be less than zero. Um, so that's gonna be between zero and 40. So right now we have two options. We could go from 0 to 20 or 20 to 40 But, um, what houses decide here is the initial problem. So he said, Are one is greater than our to or ultra. Frankly, the speed earning would be greater going anyways. Are one is greater than, aren't you? Yes. So that means our r or X value work. Ah, reader set of solutions. So the portion of bath clips here to the right hand side which could test from 20 to 40 or wrong plug, are one in for expense. Moores B. When anything is less than our one, which is less than 40 which confirms what we were trying to find in our initial problem over here. Just to reiterate our answers, um, were part a We loved it and 12 algebraic part. He figured out that neither of the rates could equal 20. So that gives us a sense for both wrote. And since both of the on rates are almost symmetrical than photograph, it's, um, the origin, which explains why both the horizontal and vertical as my toes were equal to 20 un purport. See, we just wanted to buy the conditions are one greater than our to or the speaker training would be speed going to boundary. It's which found using the polynomial inequality passes that were practicing throughout this whole traffic. So this is just an example of one. You It's a polynomial inequality. But process, for instance, Find your gas mileage. Friends. Oh, yes. Manage plans with your friends. What you're planning for trick or something like that. So yeah, that's why what we're learning.