00:01
Related rates uses derivative in order to relate the movement of one object with respect to another.
00:11
So consider a train, train s that is moving toward a station and at an instant that it is at a distance of 50 miles from north from the station, it's moving at a speed of 80 miles per hour.
00:36
So we say mph.
00:39
Another train, train w which is 20 miles west of the station is traveling west away from the station.
00:52
So at this instant it is 20 miles and it's moving farther from the station at a rate of 30 .15 miles per hour.
01:03
We want to know how fast the distance between these two trains is changing at a given instant.
01:09
So that distance is represented by this green line.
01:16
So if we try to draw a figure out of that we note that we can form a right triangle with legs of 50 and 20.
01:31
So 50 and 20.
01:33
Now for a right triangle let's say this is a and this is b.
01:38
We use pythagorean theorem in order to relate in order to relate the sides.
01:46
So we have c squared equals a squared plus b squared.
01:53
So if a is 50 and b is 20 then we can solve for c as follows.
01:59
So this new first 50 squared plus 20 squared and this gives us 2 ,900 and we take the square root and we get 53 .85...