00:01
So in this problem, man is standing next to a river.
00:06
Here's our river.
00:08
Water's flowing along.
00:10
Actually, i'll make it blue.
00:15
Water's flowing along.
00:19
And the river is one mile across.
00:26
And he's standing here at point a.
00:30
And so he can row across to point p.
00:42
And then walk over to point c like that and we're told that point b right here which is directly across from a from here to c is seven miles and we're given that he can row across there at two miles per hour and walk then at five miles per hour okay and what are we asked then? we're asked to find the total time for this trip from a to c as a function of x.
01:43
And we are given that x is this distance here from p to c.
01:53
Okay, so first of all, we notice there's a right triangle in here.
02:01
From a, a, b, p is the right triangle.
02:10
So let's use that.
02:15
So to use that, i need the distance from b to p.
02:20
Well, b to p is simply 7 minus x, right? this total distance out to c minus however far x is.
02:30
And so then on our triangle a, b, p, by the pythagorean theorem, we know that ab squared plus bp squared is equal to a .p.
02:55
Squared, right? the sum of the squares of the legs is equal to the square of the hypotenuse...