Transportation Costs (or Trucker’s Dilemma)
Math 1050 College Algebra Project
A truck driving 260 miles over a flat interstate at a constant rate of
Part I: To solve a problem like this, it is a good idea to start with calculating an actual example. We will begin by finding the total cost if the truck is driven at
A. Let’s start out by finding how long the trip will take.
The length of time required for the trip is __5.2 hours__________________. (Do not round.)
B. Now, with this time known, how much will it cost to pay the driver and run the truck?
The amount needed to pay the driver and run the truck is __$201.92__________________. (Round to nearest cent.)
C. Next determine, at
The amount of fuel required is __260/7 gallons___________________. (Do not round. Leave as a fraction.)
D. With the amount of fuel known, how much will the fuel cost to make the
The cost of the fuel is _$130.00____________________. (Round to nearest cent.)
E. Finally we can find the TOTAL cost.
The total cost for the trip is __$331.92___________________. (Round to nearest cent.)
Part II: The preceding process should have illuminated the basic procedure we will use to find the total cost of a trip. Next we will find the total cost if the truck is driven at
A. Let’s find how long the trip will take.
The length of time required for the trip is ___4 hours_________________. (Do not round.)
B. Now, with this time known, how much will it cost to pay the driver and run the truck?
The amount needed to pay the driver and run the truck is __$155.32__________________. (Round to nearest cent.)
C. Next, to begin determining the fuel cost, we need to find the mileage (miles per gallon of fuel) when the truck is travelling at
The mileage at
D. With the fuel mileage known, how much fuel will be needed for the
The amount of fuel required is __520/11 gallons___________________. (Do not round. Leave as a fraction.)
E. With the amount of fuel known, how much will the fuel cost to make the
The cost of the fuel is ___$165.45__________________. (Round to nearest cent.)
F. Finally we can find the TOTAL cost.
The total cost for the trip is ___$320.77__________________. (Round to nearest cent.)
Part III. We should now have a good process for determining the total cost of a trip for any rate of speed greater than or equal to
A. Let’s find how long the trip will take.
The length of time required for the trip is ____260/X_________________.
B. Now with this time known, how much will it cost to pay the driver and run the truck?
The amount of money needed to pay the driver and run the truck is ___260/X (38.83)__________________.
C. Next, to begin determining the fuel cost, we need to find the mileage (miles per gallon of fuel) when the truck is travelling at X miles per hour.
The mileage at X miles per hour is __12-.1X___________________.
D. With the fuel mileage known, how much fuel will be needed for the
The amount of fuel required is __260/12-.1X___________________.
E. With the amount of fuel known, how much will the fuel cost to make the
The cost of the fuel is __910/12-.1X___________________.
F. Now we can find the TOTAL cost function. Express your function as C(X) =
TOTAL Trip Cost Function is ____10095.8/X + 910/12-.1X_______________________________
G. The last thing we should do is verify that this is the correct function by evaluating it at
F(50) = ___$331.92_________________________
F(65) = __$320.77__________________________
Part IV. Assuming the function is modeling correctly, you need to calculate the minimum cost. Graph the Cost Function and find its minimum point. Sketch your graph here: Have the lower left point represent (50,315). You may use a graphing utility to help you find the minimum point.
The minimum COST for the trip is _____$319.71_______
The MPH that minimizes COST is ___$61.60__________
Reflective Writing: How did this project change the way you think about real-world math applications? Write at least one paragraph stating what ideas changed and why. Next, discuss how the math skills that you applied in this project will impact other classes you will take in your school career? Point to specific parts of the project and your own process in completing it that might have applications for other classes.
This project changed the way I think about real-world math applications by comparing it to driving. I relate to driving because it is something that I do every single day. This project really helped me discover that the rate you drive changes what mileage you get. It is actually very simple to calculate. I had to work hard and use logics to do this project. It will benefit me in my school career. It taught me to not make things harder than they need to be. Creating a graph gave me a good visual and I learned that I can make graphs in almost any of my classes to give me a better picture about how things are being presented to me.
