00:01
So for this problem, we want to keep our whole objective in mind.
00:06
So we have a swimming pool, and this is going to be a view of it, where this is the water, right? so we know that it is three feet deep.
00:17
It's going to be 40 feet long.
00:21
And then we'll have going to be a rectangular prism.
00:29
So we'll draw that real quick.
00:32
And we can see that it's going to be.
00:36
20 feet wide.
00:38
So based on this, we also see that it's three feet deep at a shallow end, but then it's nine feet deep at the deep end.
00:54
And we have a cross section shown in the figure.
00:56
So if we know the pool is being filled at a rate of 8 feet cubed per minute, so right there we want to stop.
01:03
We want to recognize this is a rate.
01:05
This is a change in volume because it's feet cubed per minute.
01:09
So this is dvdt, a change in volume with respect to time.
01:13
And that's going to equal 0 .8 feet cubed per minute.
01:19
And when we use it in our calculations, we're going to use 0 .8, as long as the units all work out.
01:26
Then we want to determine how fast the water level is rising...