00:01
A kayaker paddled 10 kilometers upstream against the current, then turned around and traveled 15 kilometers downstream with the current.
00:09
If the speed of the current was 3 miles per hour, kilometers per hour, and the upstream trip took 30 minutes longer, what was the speed of the kayaker without the speed of the current? so what we want to know is we're looking for the speed of the kayaker.
00:24
We're going to let that be x.
00:26
So how fast is he paddling? so let's see what happens with and without the current.
00:30
With the current, that means that his rate is going to be x plus the speed of the current, which is three kilometers per hour.
00:40
When he's going upstream, it's going to be x minus three kilometers per hour because he's having to work against the stream.
00:48
So this is going to be our distance.
00:53
This is going to be our rate.
00:55
This is my distance.
00:57
This is my rate.
00:58
Now, we also know something, we have a relationship between the time.
01:04
We know that the upstream trip took 30 minutes longer.
01:11
So we know the time to go downstream is the same as the time to go upstream plus a half an hour.
01:20
I don't want to do 30 minutes.
01:21
I want to do half an hour.
01:23
So how are we going to get that? well, we know that we have distance equals rate times time.
01:29
Which means our time is going to be our distance divided by our rate.
01:33
So we're going to look at the red, at the blue here.
01:37
We're going to have what's going to be distance divided by our rate plus five.
01:44
That's the blue time.
01:46
Now the red is going to be the distance, 15, divided by x plus three.
01:53
So when we solve this equation for x, we're going to have the rate that he was paddling.
01:57
So how do we do that? multiply by the least common denominator, which is x plus 3 and x minus 3.
02:05
So i'm going to say x plus 3, x minus 3, x plus 3, x minus 3, x plus 3, x plus 3, and x minus 3...