Once Ted is able to calculate the area of the pool, he locates the number again for Pool Water, Inc., and is just about to call when he realizes something. The pool hasn't been used, filled, or cleaned in several months. If he adds water now, the local kids will be swimming in a soupy mixture of water, leaves, and dirt.
Ted finds the number for the pool cleaning company that the community used the year before. When he calls them, the first thing they want to know (of course!) is how densely the leaves cover the pool. Apparently, that information will help them decide how many people to send out to the pool and approximately how long the job will take.
Ted has heard about density before, but he can't remember what it is exactly or how it's calculated. Ted decides to hang up and do a little more research so that he can give the company an accurate measurement for their estimate. Fortunately, Ted finds a video online that will help him determine the density of debris in the pool. Watch the video below to improve your own knowledge of density.
As you watch this video, use the study guide to follow along if you'd like. Click the button below to download the study guide.
Density is a rate that measures one quantity against another unit of measure. In a way, it tells us the compactness of a substance inside a particular space. For example, the following rates are measures of density. Thirty-three fire hydrants per square mile, 12 pounds of apples per basket, zero point five pumpkins per pie, and one hundred leaves per square foot.
Density can be recorded as a fraction or decimal. For example, if Ted counted one thousand two hundred fifty-five leaves in a space of ten square feet, we could reduce this fraction to two hundred fifty-one leaves for every two feet. This was accomplished by factoring a five from both the numerator and the denominator. Rather than simplifying fractions, we could simply divide the numerator by the denominator. Suppose Ted went on to count nine thousand seven hundred fifty leaves in seventy-eight square feet, then the division of these two numbers leaves us with one hundred twenty-five leaves per square foot. Notice the unit of measure here, leaves per square foot. This is the same unit of measure had we just divided our first example into a decimal rather than reducing the fraction or at least it is very close. One thousand two hundred fifty-five leaves divided by ten square feet is one hundred twenty-five point five leaves per square foot.
Let's practice a few more. Suppose Freddie counted 361 road reflectors while riding the bus eight miles to school. What is the reflector density in terms of reflectors per mile? Well, three hundred sixty-one reflectors divided by eight miles is forty-five point one two five reflectors per mile. Now you try the following three. Resume video playback in a moment to check your work… Sarah packed twelve point seven pounds of apples in three bags and achieved a density of four point two three three rounded pounds per bag. The population density question was a bit more difficult to calculate since we needed to find the area of the county first. The area of the county is one hundred ninety-two square miles. The population total divided by this number results in a population density of twenty-one thousand two hundred thirteen people per square mile. Finally, the French fries order density was four hundred fifty-five point two five French fries per order.
Question
What does Ted need to tell the folks at A Cleaner Pool, to get an accurate estimate on their service?
