00:01
For this problem, we're told that we have a tire with a radius of 12 inches, and we're doing 320 revolutions per minute.
00:07
We need to know what the linear speed is in miles per hour.
00:10
So one thing to remember here is that one revolution is equivalent to a length of circumference.
00:16
So if the radius is 12, then the circumference is going to be the 2 times 12, which is 24 times pi.
00:23
So this is what we need to use for our conversion.
00:26
So let's start off, we have 320 revolutions per minute.
00:30
Minute, so that's going to be over one minute.
00:33
We're trying to figure out miles per hour.
00:35
So let's go ahead and first convert the revolutions.
00:38
So our goal is to get rid of the revolution.
00:40
So i'm going to put one revolution in the denominator.
00:43
At the top, i'm going to put the units here, or the circumference.
00:47
Now, this is in inches.
00:48
Our goal is to get to miles.
00:50
So i'm going to convert this to feet.
00:52
So there is 12 inches and one foot.
00:54
So i'm going to do one foot over 12 inches.
00:57
Then from there, i'm going to multiply the number of feet, which is 5 ,280 feet in one mile.
01:05
So what will happen here is that the minutes will cancel, not the minutes, the revolutions will cancel with the revolutions, inches with inches, and feet with feet.
01:14
So right now we're in miles per minute...