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 let's say it's in Zac where's my pen go oh I'm using the wrong tool okay so let's say I had Zack and they're driving at a speed of let me see a twenty eight feet feet per minute so what I'm going to ask you is if he's going twenty eight feet in every minute how many inches will Zack travel in one 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 twenty eight and I'll write ft short for feet feet per minute and I'll write min short for minutes 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 and if you didn't know that you do now so we know that there are 12 inches per foot so if he's going 28 feet per minute he's going to be going 12 times that many inches per minute so 12 times 28 let's see let me do the little work down here 28 times 12 well 16:56 and 280 I probably shouldn't be doing this messy and this kind of stuff it's it'd be okay to use a calculator although it's always good to do the math yourself it's good practice so that's six five plus eight is 13300 36 so that equals three hundred and thirty-six inches per minute and something interesting happened here is that you notice 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 that you have the same number in the numerator and you have the same number of denominator and you're multiplying not adding you can cancel them out so the feet and the feet cancelled 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 that's inches inches per foot and because the foot per minute came from here and the inches per foot came from here and then I'll just cancel this out and I would have got 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 at many inches per minute right because there are 12 inches per foot so I'm going 36 336 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 in one second so let me erase some of the stuff here at the bottom let me erase this because that's just probably just going to confuse everybody accelerates this to okay so I'm going to be going so 336 336 inches let's try it like that inches per minute and I want to know how many inches per second well what do we know we know that one minute and notice I write it in the numerator here because I want to cancel it out with this minute here one minute is equal to how many seconds it equals 60 seconds right and and just this is this part can be confusing but it is 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 I'm going to travel in one second I'm not going to travel more than 336 or am I going to travel less than 300 36 inches per second well obviously less because the 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 lower distance if I'm 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 and I know this can be very confusing in the beginning but that's why I always want you to think about should I be - should I be getting a larger number or should I be getting a smaller number and that'll 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 a minutes in the denominator in the units here we want two minutes in the numerator here and a seconds in the denominator here and one 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 and excuse me and now if I were to actually divide this out we could see actually we could just divide the numerator in the denominator by 6 6 goes into 336 156 times 56 over 10 and lo we could divide that again by 2 so then that gets us 28 over 5 and 20 8 over 5 let's see 5 goes into 28 5 times 25 3 5 point 6 so this equals 5 point 6 so we I think we now just solve the problem if Zack is going 28 feet in every minute that's the speed he's actually going 5 point 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 so how many if we want to say how many miles that is should we be dividing or should we be multiplying what we should be dividing this is going to be a smaller number of miles and we know that there that one mile is equal to and you might want to smell is 5280 feet is actually a pretty useful number to know and then that will actually cancel out the feet and 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 is 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 minutes 60 seconds per minute and 60 minutes per hour so 3,600 over 1 seconds per hour and these seconds will cancel out and then we're just left with we just multiply everything out we get in the numerator 91 times 3600 right 91 times 1 times 3600 in the denominator we just have 5,280 and 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 a calculator let's see so if I say 91 times 3600 whoops I messed up 91 times 3600 that equals a huge number divided by 5,280 oh man I keep Cina 91 times 3,600 / 5200 the calculus I think my mouse is missed let me tell you if I could type it 91 times 3600 divided by 5,280 60 to 0.05 so that equals 62 point oh five miles per hour