An Olympic marathoner passes the seven kilometer point of race after 21 minutes and reaches the 22 kilometer point after 2.7 hours. Find the average speed in the marathoner in kilometers per hour. So the first thing we want to realize is if we're trying to get it in kilometers per hour, we know that for slope, it's always rise over won't run. So our Y is going to be kilometers and our X is going to be hours. So our point XY is going to be in terms of hours, then kilometers. So the given information, the first piece is 21 minutes. Oh wait, I can't have minutes here because I needed hours. So we need to convert 21 minutes to hours. The easiest way to do that is to think about the fact that one hour is 60 minutes. If we think about multiplying by one hour over 60 minutes, then the minutes in the numerator and the minutes in the denominator will cancel, leaving us the unit of hours. Remember that 21 minutes could be thought as being over an understood one, so we get twenty 160th hours. Well, both those numbers are divisible by three, so we're really going to reduce it to 720th hours. So in our first point, we're going to have A7 twentieths our hours to seven kilometers. Our second point is 2.7 hours. It's already given an hours to 22 kilometers. So now when we do our our slope, our change of YS over change of XS or our kilometers over our time and hours, we have 22 -, 7 / 2.7 -7 twentieth. Now the reality is I could choose either of the YS to come first and either of the XS to come first. The big piece with that is that the ones that are right on top of each other have to come from the same point. So 22 / 2.7, those needed to be from the same point and we can see that they really work. So continuing with our math, 22 -, 7 is going to give us 15, this 2.7 -, 7 twentieth, that's going to give us a little bit of a problem because we don't usually do decimals with fractions. So let's change that 2.7 into 2 7/10 because .7 just means 7/10. When we change that, we going to get 27 tenths to get that into an improper fraction, 2 * 1020 plus the seven. Now when we look back here at the denominators, we'd have 27 tenths, but we have 7 twentieths. Well, we can't combine 2 fractions with addition and subtraction unless they have common denominators. So we're going to take this fraction here, and to get them both to be twentieths, we're going to multiply by a 2 / 2. So 27 * 2 is 5410 * 2 is 20. So this 27 tense is really the same thing as 54 twentieths. And then we're going to take away 7 twentieths and that's still in the denominator with 15 in the numerator. So 54 - 7 is going to give us 47. So we have 15 / 47 twentieths. Now improper fraction, we have 15 really being divided by 47 twentieths, and so that 15 is understood over one and we're going to multiply it by 20 / 47. So at this point 15 * 20 is 300 / 47. Now the directions actually ask us around to the nearest hundredth. So I'm going to grab my calculator at this point and I'm going to put it into the calculator. We could have also done long division, 6.3829787... According to my calculator, 100th, 100th means 2 decimal places. So here's my tenths, here's my hundredths and order to round. We look one place past what we want. If it's a zero to four, we're just going to drop the rest of the number off. It's a two, so we're going to drop it off. Our final answer is going to be 6.38. If it had been a 5 through 9, we would have rounded that eight up by one place.