University:
University of Arkansas
Course:
CHEM 1053 | Chemistry in the Modern World
Academic year:

2023
Views:

313

Pages:

2
Author:

madeleinejames20

In this example, we'll work a problem where we'll use the basics of dimensional analysis to solve a word problem. The first thing we'll want to do is sort the information that we're given as we read through the problem. You're planning on driving with three friends to Party Ville, Wisconsin for spring break, which is 750 miles one way. So from this information, we know there are going to be four people and that 750 miles equals one way. Your van averages 15 miles per gallon, so we know that 15 miles equals one gallon. The average cost for gasoline is three dollars and 50 cents per gallon, so three dollars and fifty cents will equal one gallon. How much will each person need to pay toward gas for the trip there and back, assuming the cost is evenly divided? From this, we know that we want two ways (both there and back) for their trip. The next step is to come up with a plan of how to use the information we have here along with the conversion factors that are given in the problem to get to the solution of dollars per person. We can start our dimensional analysis with ways and convert from ways to miles using the conversion factor one way equals 750 miles. Then we can convert from miles into gallons using the conversion factor of 15 miles equals one gallon. Then we can convert from gallons to dollars using the conversion factor one gallon equals three dollars and fifty cents. And finally, we can convert to dollars per person using the information of four people. Let's look at the dimensional analysis. We begin with two ways because Waze is on the top. We'll want to put ways on the bottom from the conversion factor one way equals 750 miles. In this way, we can cancel ways and our units are now miles. Now we want to get rid of miles, so we'll have to put it on the bottom when we use the conversion factor one gallon equals 15 miles. In this way, miles also cancels and we now have units of gallons. Next, we'll want to convert from gallons to dollars because gallons is now on top. To get rid of gallons, we'll have to put it on the bottom when we use the conversion factor one gallon equals three dollars and fifty cents. Gallons will cancel, and we're left with dollars. Now we'll need to convert from dollars to dollars per person because we want to keep dollars. We'll only use the information for persons and multiply by 1/4 persons because we want dollars per person as our units in the solution. When we multiply and divide all of these numbers, we should come up with the answer eightyseven point five zero, and the units are dollars per person.