00:01
Our question says to consider a 20 -mile bike ride.
00:03
So i say the total distance x -sub -t is 20 miles, and it's broken into two parts.
00:09
You ride the first 10 miles.
00:11
So since it's broken into two parts, x -1 is 10 miles and x -sub -2 is 10 miles, and you combine them together, you get the total of 20 miles.
00:19
And we're told we ride the first 10 miles with an average velocity of 8 miles per hour.
00:24
So i say v -1, and then you put a bar over it for average.
00:27
That's one way of representing average.
00:29
So v .1 is 8 miles per hour.
00:32
And then it says to figure out the total speed over the next 10 miles in order to have for part a a total average velocity, v .t, and then i put a bar again over it to represent average of 4 miles per hour.
00:47
Okay, so to do that, we first need to figure out the time it's going to take to travel the first 10 miles, and then we can figure out the time it's going to take to travel the second 10 miles.
00:59
And figure out the average velocity over that second 10 miles.
01:02
So the time we find for the first 10 miles is going to be true in every case, because we know the average speed over that first 10 miles.
01:10
So by definition, t1, the time it takes to travel the first 10 miles is just going to be equal to the distance x1 divided by the average speed v sub 1 bar.
01:22
Plugging those values in, we find that this is equal to 1 .25 hours.
01:27
Ok.
01:29
Well, if we look at the equation for, total average speed, this is just going to be equal to the total distance x sub t divided by the total time, which would be the time to travel the first 10 miles, t1, plus the time to travel the second 10 miles, t2.
01:46
Therefore, we can rearrange this to solve for t1 plus t2.
01:50
We find that t1 plus t2 is equal to the total distance, x sub t, divided by the average velocity over that distance.
02:00
So we plug in 20 meters for x sub t and 4 miles or 20 miles for x of t and 4 miles per hour for v sub t we find that the time t 1 plus t 2 is equal to 5 hours therefore since t 1 plus t 2 is equal to 5 hours 2 would be 5 hours minus t 1 .25 hours or in other words t 2 is equal to 3 .75 hours well now that we know the time it takes to travel the distance of 10 miles or x sub 2 we can find the average velocity over that distance, which we call v sub 2 bar.
02:46
This is just simply x sub 2 divided by t sub 2.
02:52
So plugging those values in, we find that the average velocity over the second 10 miles is 2 .67 miles per hour.
03:06
This can be boxed in as our solution for part a.
03:11
Part b is very similar, but instead of using the average velocity of four miles per hour, we're going to do the same thing for an average velocity, of 12 miles per hour.
03:28
Again, we have the same equation for t1 plus t2.
03:33
So we have t1 plus t2 is equal to the total distance x sub t, divided by the average velocity over that distance, v sub t...