00:02
So we are told we have a 50 milliliter vial that contains a drug and the concentration is in milligrams per milliliter.
00:14
It is added to 100 milliliters of water and it will be distributed through an iv.
00:25
The iv is set up to deliver 15 drops per millimeter and we need to know how many drops.
00:36
How many drops per minute to deliver 25 milligrams of the drug per hour.
00:56
So the first step of this problem is to combine these two values.
01:02
So we have 15 milliliters plus 100 millimeters equals 150 millimeters.
01:14
And in this 150 milliliters, we know that the drug contains 1 ,000, milligram per milliliter.
01:25
Since we were given 50 milliliters of the drug initially, we know that there are 50 milligrams per 150 milliliters.
01:40
So we can reduce this down, divide by 50, and we'll get one milligram per three milliliters.
01:51
Now let's work with this value here.
01:54
We have 25 milligrams of the drug per hour.
02:00
We need to get to drops per minute.
02:03
So let's convert this hours to minutes.
02:07
So we have one hour equals 60 minutes.
02:14
And this gets rid of our hours and we're left with a minute.
02:17
So we're left with milligrams over minutes.
02:21
Now we have to get to drops.
02:23
Well, we know the iv gives 15 drops per milliliter and we know that the drug is in one milligram per three milliliters.
02:34
So to get rid of the milligrams we're going to use this conversion right here.
02:40
So for every one milligram, you're going to have to deliver three milliliters of the solution.
02:47
Now we are, so milligrams cancels out.
02:50
Now we are in milliliters per minute, but we know that there are 15 drops per milliliter.
02:58
So for every one milliliter, we're going to need 15 drops.
03:05
Milliliters cancels out and we're left with drops per minute.
03:11
So let's do that now...