You receive an order for five milliunits per minute.
The solution is labeled ten units per liter. What is the correct flow rate in milliliters per hour?
So to find the correct flow rate, we'll have to perform several conversions. Notice how the order is given in milliunits per minute
The solution is given as units per liter.
And the flow rate is mils per hour.
We'll solve this problem using proportions. Let's begin by converting the given order, in milliunits per minute, to milliunits per hour.
But to set up the proportion, we'll compare milliunits to minutes.
So we'll begin with the rate of five milliunits per minute. So five milliunits per one minute
must be equal to the number of milliunits per hour . So we have an unknown number of milliunits, we'll call it X milliunits, per one hour.
But because we know we have to have the same units on the top and the same units on the bottom,
instead of writing one hour here, since one hour equals sixty minutes, write this as sixty minutes.
So if we find X, we'll know the number of milliunits per hour.
Again, it's important to recognize that we have the same units on the top and the same units on the bottom.
If we didn't have this, we'd have to perform a conversion first.
So here we have one times X must equal five times sixty.
Well one times X is X. Five times sixty is three hundred, which means the given order could also be written as
three hundred milliunits per hour.
Now for the next step, let's determine how many units we need per hour.
So we'll set up another proportion.
Three hundred milliunits
is to an unknown number of units, we'll call it Y units, must be equal to
The conversion between milliunits and units is given here: one thousand milliunits equals one unit.
This wil give us the second half of the proportion.
One thousand milliunits
is to one unit.
Again, notice how we have the same units on the top and the same units on the bottom, so now we can cross-multiply and solve for Y.
So we have Y times one thousand, or one thousand Y, must equal three hundred times one, or three hundred.
Divide both sides by one thousand.
Three hundred divided by one thousand is equal to three-tenths, or zero point three.
Which means now we can say that the order
is zero point three units per hour.
So now the last step is to determine how many milliliters we need per hour.
So we'll set up a third proportion.
Zero point three units per an unknown number of milliliters, we'll call it Z milliliters
must be equal to the solution rate of ten units
per one liter.
But again, notice how we have milliliters in the denominator here
so we also want milliliters here.
So instead of writing one liter, we'll use a conversion that one liter equals on thousand millliliters.
So we have one thousand milliliters here.
And now that we do have the same units on the top and on the bottom, we can finally cross-multiply and solve for Z
which will tell us the number of milliliters we need for this order and, therefore, the number of milliliters needed per hour.
So we have Z times ten, that's ten Z, must equal zero point three times one thousand, that would be three hundred.
Dividing both sides by ten,
we have Z equals thirty.
Which means if the order is zero point three units per hour, that means the order requires thirty milliliters per hour.
I hope you found this explanation helpful.