>> In this video we are going to solve some uniform motion problems and I already went
over in the first video how we got the pictures and so now we are going to continue
to completely solve some problems.
So, remember the formula though, rate times time equals distance.
This was the first problem we looked at, 2 cyclists started
at the same corner and ride in opposite directions.
One cyclist rides twice as fast as the other,
in 3 hours they are 81 miles apart, find the rate of each cyclist.
So, we decided this was the picture, they started from the same spot,
went in opposite direction and eventually they end up 81 miles apart from each other.
So now we need to set up some variables and I want to use a chart to do this.
So, I am going to have cyclist-1 and cyclist-2, one is going to be faster than the other
and I am going to put something in for their rate and something in for their time.
And then their distance, we are going to get by multiplying rate times time.
So, what do we know, one cyclist rides twice as fast, so the speed is twice
as fast, the rate is twice as fast.
So, let us say the first cyclist is going x miles per hour
and then the other cyclist would be going 2x miles per hour.
What do we know about their time?
Well, we are assuming they are leaving at the same time because it doesn't say
anything else and that they are going for 3 hours,
so each of them travels for 3 hours, that is their time.
So, rate times time equals distance and that is 3x and this is 3 times 2x which is 6x.
So, now I could go up and put this on the picture.
We move this a little bit down, okay.
So, cyclist-1 now, the whole idea of this picture is I want to put
in the distance that I get for each.
So, this is 3x, that distance right here, and the distance for cyclist-2 is 6x.
Now, we look at the picture, this piece plus this piece must equal the total of 81
and that is your equation, 3x plus 6x is 81.
We go down here, 3x plus 6x equals 81, 9x is 81, divide both sides by 9, so x is 9.
Alright now, what does x stand for, x stands for the rate of cyclist-1.
So, we are going to now actually fill in the real numbers into the chart.
For cyclist-1 there is a rate, and a time, and a distance.
So we have got for cyclist-1 we have got 9, so cyclist-2, at 2x would be 18.
They each went 3 hours, so their distance rate times time equals distance is
for the cyclist-1 would be 27 and the cyclist-2 would be 54.
This is sort of like your check.
So, now let us see would it be true on that picture that cyclist-1 went 27 miles
and cyclist-2 went 54 and let us see, 27, 54, will they end up being 81 miles apart
from each other, sure, because 27 plus 54 is 81.
Alright, now let us see what the question is.
Find the rate of each cyclist?
Okay, so the rates are 9 miles per hour and 18 miles per hour.
What is nice about this little chart in the end,
if it would have asked you something different like, how far did the cyclist,
the slower cyclist go and you could see it, 27 miles.
How far did the second cyclist go, 54 miles.
What if it just asked for the rate of the faster cyclist, it would be 18 miles an hour.
The rate of the slower cyclist would be 9 miles an hour.
All your information is right here in this chart, all the info you need to check
and to answer any questions you might be asked.