Speed translation

Welcome to the presentation on units. Let's get started. So if I were to tell you -- let me make sure my pen is set up right -- if I were to tell you that someone is, let's say they're driving at a speed of -- let's say it's Zack. So let's say I have Zack. And they're driving at a speed of, let me say, 28 feet per minute. So what I'm going to ask you is if he's going 28 feet in every minute, how many inches will Zack travel in 1 second? So how many inches per second is he going to be going? Let's try to figure this one out. So let's say if I had 28, and I'll write ft short for feet, feet per minute, and I'll write min short for a minute. So 28 feet per minute, let's first figure out how many inches per minute that is. Well, we know that there are 12 inches per foot, right? If you didn't know that you do now. So we know that there are 12 inches per foot. So if you're going 28 feet per minute, he's going to be going 12 times that many inches per minute. So, 12 times 28 -- let me do the little work down here -- 28 times 12 is 16, 56 into 280. I probably shouldn't be doing it this messy. And this kind of stuff it would be OK to use a calculator, although it's always good to do the math yourself, it's good practice. So that's 6, 5 plus 8 is 13. 336. So that equals 336 inches per minute. And something interesting happened here is that you noticed that I had a foot in the numerator here, and I had a foot in the denominator here. So you can actually treat units just the same way that you would treat actual numbers or variables. You have the same number in the numerator and you have the same number in the denominator, and your multiplying not adding, you can cancel them out. So the feet and the feet canceled out and that's why we were left with inches per minute. I could have also written this as 336 foot per minute times inches per foot. Because the foot per minute came from here, and the inches per foot came from here. Then I'll just cancel this out and I would have gotten inches per minute. So anyway, I don't want to confuse you too much with all of that unit cancellation stuff. The bottom line is you just remember, well if I'm going 28 feet per minute, I'm going to go 12 times that many inches per minute, right, because there are 12 inches per foot. So I'm going 336 inches per minute. So now I have the question, but we're not done, because the question is how many inches am I going to be traveling in 1 second. So let me erase some of the stuff here at the bottom. So 336 inches -- let's write it like that -- inches per minute, and I want to know how many inches per second. Well what do we know? We know that 1 minute -- and notice, I write it in the numerator here because I want to cancel it out with this minute here. 1 minute is equal to how many seconds? It equals 60 seconds. And this part can be confusing, but it's always good to just take a step back and think about what I'm doing. If I'm going to be going 336 inches per minute, how many inches am I going to travel in 1 second? Am I going to travel more than 336 or am I going to travel less than 336 inches per second. Well obviously less, because a second is a much shorter period of time. So if I'm in a much shorter period of time, I'm going to be traveling a much shorter distance, if I'm going the same speed. So I should be dividing by a number, which makes sense. I'm going to be dividing by 60. I know this can be very confusing at the beginning, but that's why I always want you to think about should I be getting a larger number or should I be getting a smaller number and that will always give you a good reality check. And if you just want to look at how it turns out in terms of units, we know from the problem that we want this minutes to cancel out with something and get into seconds. So if we have minutes in the denominator in the units here, we want the minutes in the numerator here, and the seconds in the denominator here. And 1 minute is equal to 60 seconds. So here, once again, the minutes and the minutes cancel out. And we get 336 over 60 inches per second. Now if I were to actually divide this out, actually we could just divide the numerator and the denominator by 6. 6 goes into 336, what, 56 times? 56 over 10, and then we can divide that again by 2. So then that gets us 28 over 5. And 28 over 5 -- let's see, 5 goes into 28 five times, 25. 3, 5.6. So this equals 5.6. So I think we now just solved the problem. If Zack is going 28 feet in every minute, that's his speed, he's actually going 5.6 inches per second. Hopefully that kind of made sense. Let's try to see if we could do another one. If I'm going 91 feet per second, how many miles per hour is that? Well, 91 feet per second. If we want to say how many miles that is, should we be dividing or should we be multiplying? We should be dividing because it's going to be a smaller number of miles. We know that 1 mile is equal to -- and you might want to just memorize this -- 5,280 feet. It's actually a pretty useful number to know. And then that will actually cancel out the feet. Then we want to go from seconds to hours, right? So, if we go from seconds to hours, if I can travel 91 feet per second, how many will I travel in an hour, I'm going to be getting a larger number because an hour's a much larger period of time than a second. And how many seconds are there in an hour? Well, there are 3,600 seconds in an hour. 60 seconds per minute and 60 minutes per hour. So 3,600 over 1 seconds per hour. And these seconds will cancel out. Then we're just left with, we just multiply everything out. We get in the numerator, 91 times 3,600, right? 91 times 1 times 3,600. In the denominator we just have 5,280. This time around I'm actually going to use a calculator -- let me bring up the calculator just to show you that I'm using the calculator. Let's see, so if I say 91 times 3,600, that equals a huge number divided by 5,280. Let me see if I can type it. 91 times 3,600 divided by 5,280 -- 62.05. So that equals 62.05 miles per hour.