00:01
In this problem, we're asked to find the speed of the current of a river.
00:06
If we know that a boat took seven hours to make the total trip, and that means upstream and downstream.
00:15
Now, the speed of the boat by itself is 14 miles per hour, and the distance one way is 33 miles.
00:21
So we're going to let c represent the speed of the current.
00:24
T be the time upstream, and then 7 minus t has to be the time downstream.
00:30
So we really have two equations with two variables.
00:33
We're using distance equals rate times time.
00:37
So our time times 14 minus c equals 33, that takes care of the distance upstream.
00:49
Because 14 minus c, the current would actually be making the boat go slower.
00:55
And then for the distance downstream, our time would be.
01:00
7 minus t times its rate 14 plus c.
01:06
Now since both of those are equal to 33, we can set those expressions equal to each other.
01:13
So we're going to write t times 14 minus c equals the 7 minus t times the 14 plus c.
01:24
Do a little simplifying.
01:26
We'll get 14t minus c t equals.
01:33
98 plus 7c minus 14 t and then minus c t now because we have a negative ct here and a negative ct here we can cancel those out let's go ahead and bring this minus 14 let's go ahead and add it to both sides and now we get 28 t equals 98 plus 7c we're trying to get one of our variables in terms of the other.
02:06
If we subtract 98 from both sides, we get 28t minus 98 equals 7c.
02:12
And then when we divide everything by 7, we get 4t minus 14 equals c.
02:21
Now that gives us an equation for c in terms of the t.
02:28
So we're going to take that 4t minus 14, and we're going to plug it in one of these equations here to figure out the value of c.
02:39
Well, this one looks easier, so let's do that one.
02:47
So i'm going to write t times 14 minus, but remember c now is 14 minus 14.
02:58
So in parentheses, i'll write 14 minus 14, and that equals 33.
03:08
Remember, we are taking this equation, and we're plugging in 14 minus 14 in place of c.
03:15
Let's do some simplifying.
03:20
Inside the parentheses here, i have 14 minus negative 14, so that's 14 plus 14...