Project: Planning a Trip

Planning a Trip

Introduction

There are many things to consider when planning a trip. In this project, you will explore how to plan for a trip and determine the actual cost of traveling to and from your vacation destination.

Task

Working together with your group, you will explore the rate at which you must travel to arrive at your vacation destination, a reasonable plan for travel, and costs associated with travel. Finally, using all that your group has learned, you will make an itinerary for each day of your trip. You will create a poster presentation of your trip to serve as an advertisement, so your group can recommend it to others.

Instructions

Solve each problem in order and save your work along the way, as you will create a professional advertisement at the conclusion of the project. If required, round to the hundredths place (two decimal places).

· First problem:

· Your group will be taking a road trip. You need to determine a destination at a distance of between 1000-1500 miles. You should go to a website, such as www.randmcnally.com/ or www.mapquest.com/, to find a map, driving directions, and estimated travel time. Print these resources as they will be needed in your project. Record the information in the table below.

Hint: If your estimated time is in hours and minutes, divide the minute portion by 60, so it is part of an hour, and then add that to the number of hours.

· Your group will need to decide the type of vehicle that you want to use for travel. If there are four or five people, make sure there is enough room for yourselves and your luggage. Use a website such as www.fueleconomy.gov to find the EPA Estimated Fuel Economy for your vehicle and the fuel tank size. Since most of your driving will be on a highway, record the highway fuel economy for your vehicle in the table below.

Beginning Trip Information

Starting Location of Trip
Vacation Destination
Total Miles
Estimated Time to Destination (in hours)
Vehicle Type
Estimated Fuel Economy (miles per gallon for highway driving)
Size of Fuel Tank (in gallons)
Number of People taking the Trip

· Based on the estimated time to the destination shown in your table, calculate the average rate at which you must travel to arrive at your destination.

Hint: To find the average rate of your travel, you will need to use the formula where D is the distance, r is the rate (speed), and t is the time.

· Many times when you travel by car, there is road construction or slow traffic. You want to determine how long it would take you to arrive at your destination if your average rate is different from what you calculated. Calculate your estimated time to your destination based on the rates given in the table below, comparing each value to that for 55 miles per hour to see how much time you save by driving faster.

Hint: You will need to use the formula to calculate the time to destination for each average rate.

Changing the Average Rate

Average Rate (in miles per hour)	Time to Destination (in hours)	Comparison of Time to that for 55 miles per hour (Time – Time for 55 mph)
55		0
60
65
70

· Using your results from changing the average rate, make a statement describing the effect of increasing your average rate. Be sure to comment on the significance of the sign of your numbers in the third column.

· Second problem:

· With a long trip, it is wise to have a plan for how far or long you want to travel in one day. Many people will try to travel 500 miles in a day. You need to determine the number of days you will be traveling and how long you will be driving each day if 500 miles per day is your goal.

Goal of 500 Miles in a Day

Average Rate (in miles per hour)	Time Driving Per Day (in hours)
55
60
65
70

Number of Days of Travel __________________________

· Some drivers prefer to only have 8 hours of driving in a day. You need to determine how many days and how far you will be driving each day if 8 hours per day is your goal.

Hint: To find the distance traveled, use the formula Then calculate the number of days by dividing the total distance by the distance traveled per day.

Goal of 8 Hours of Driving Time in a Day

Average Rate (in miles per hour)	Distance Traveled per day (in miles)	Number of Days of Travel
55
60
65
70

· Your group needs to use your calculations to make a decision whether you want to travel either 500 miles per day or a total of 8 hours of driving time. You should think about what your goal is in terms of how far or long to drive per day and a reasonable rate of travel. Be able to defend your choices.

· Based on your decision for travel, determine, the number of days it will take you to reach your destination, how many days you want to stay at your destination, and the number of days for your return trip home (it should be the same number of days as it took to reach your destination). Then, calculate the total number of days you will be on vacation.

Decision for travel (including average rate):

Number of Days to Reach Destination ___________

Number of Days Staying at Destination __________

Number of Days to Return Home ____________

Total Number of Days on Vacation: _______________

· Third Problem:

· You will need to rent the vehicle that you have decided to travel with. The car rental place has two different offers:

Offer #1: $10 per day, first 100 miles are free, after the first 100 miles, they charge $0.20 per mile.

Offer #2: $25 per day, all miles are charged at the rate of $0.15 per mile, and if you keep the car for more than 1 week, they take $50 off your total bill.

Write an expression for computing the cost of the car rental for each of the above options. Use d to represent the number of days and m to represent the number of miles driven.

Offer #1

Scenario	Expression for Cost
Under 100 Miles Driven
Over 100 Miles Driven

Offer #2

Scenario	Expression for Cost
Under 1 Week
Over 1 Week

· For your trip, calculate the cost for each offer and determine the best offer for your vacation.

Finally, determine the per day cost of renting the car.

Hint: You will need to calculate the cost for the entire trip meaning that you will have to double your mileage. Then, estimate how many miles you think you will travel at your destination. Finally, calculate the total mileage of the trip. Use this number and the number of days of travel from Problem #2, to calculate the cost of renting a car.

To find the per day cost of renting the car, use the formula

· You will also have to purchase gas for the entire trip. You will need to calculate the amount and cost of fuel based on your mileage and estimated fuel efficiency from Problem #1. Use $2.70 per gallon for the cost of gas.

Hint: Calculate the fuel needed by determining total mileage divided by fuel efficiency.

· The last expenses for your trip are food and lodging. Estimate how much you will spend on food per day. Be reasonable in your estimates. On average lodging is $100 per night for a single room with double beds. If your group is larger than 4 people, you will need to have two rooms. Calculate the daily cost for food and lodging and then the total cost for food and lodging based on the number of days in your trip.

· Finally, determine how much money each person in your group should contribute to the trip.

· Fourth problem:

· Finally, your group will use all of the information that you have gathered and determine an itinerary for the trip. You will need to calculate how many miles you can drive before stopping for gas. Use the size of your fuel tank and fuel efficiency from Problem #1 to calculate this. Remember you do not want to run out of gas, so leave some gallons of gas in the fuel tank.

· You will need to use your map to figure out the starting and ending location for each day. Fill out the itinerary chart on the next page.

· Now, fill out the checkbook for each day of your trip. You should be able to get the beginning balance from Problem #3. Your beginning balance will be positive, but each day’s cost should be recorded as a negative number. Record your new balance in the right-hand column for each day.

· Make a sales-pitch recommending the trip.

Itinerary Chart


	Day__	Day__	Day__	Day__	Day__	Day__	Day__
Goal for the Day (Miles)
Total Time (Hours)
Start Location
Planned Stops
End Location
Average Rate of Travel
Total Daily Cost:
Gas
Food
Lodging
Car Rental

Checkbook

Beginning Balance (Total Money Contributed by All Members of the Group)			$
Day Number	Description of Expenses (gas, food, lodging and/or car rental)	Total Cost (these should be negative)	Balance
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$
		$	$

Collaboration

Get together with another group to compare your answers to each of the four problems. Discuss how your group decided to travel, costs for food, number of days at vacation spot and explain your trip itinerary. Some groups may have more than four members, so this should be taken into account.

· What if you wanted to stop at destinations along the way of your trip? How would this affect your plans?

· What is a reasonable amount of time and distance to travel per day?

· What happens if someone wants his or her own lodging? How could you recalculate the price per person?

· Do some Internet research to determine how much it costs to travel in a different way (train, plane, or bus). Determine if another mode of transportation would lower the cost of the trip.

Conclusions

Your advertisement should be a presentation of your trip that would allure other people to join in. It should be on a poster board highlighting the itinerary and costs associated with the trip. It should include all of the mathematics used to solve the four problems above. You may either neatly write out the tables or use software such as Microsoft Word to create a professional computer generated product. You may want to include pictures of the map and destination to make it colorful.

Grade

Your project should correctly identify and justify mathematically: (1) the rate at which you must travel, (2) a reasonable plan for travel, (3) costs associated with travel, and (4) the itinerary for each day of the trip.

Score

Content

Presentation/Communication

• The solution shows a deep understanding of the problem including the ability to identify the appropriate mathematical concepts and the information necessary for its solution.

• The solution completely addresses all mathematical components presented in the task.

• The solution puts to use the underlying mathematical concepts upon which the task is designed and applies procedures accurately to correctly solve the problem and verify the results.

• Mathematically relevant observations and/or connections are made.

• There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.

• Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem.

• There is precise and appropriate use of mathematical terminology and notation.

• Your project is professional looking with graphics and effective use of color.

• The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution.

• The solution addresses all of the mathematical components presented in the task.

• The student uses a strategy that includes mathematical procedures and some mathematical reasoning that leads to a solution of the problem.

• Most parts of the project are correct with only minor mathematical errors.

• There is a clear explanation.

• There is appropriate use of accurate mathematical representation.

• There is effective use of mathematical terminology and notation.

• Your project is neat with graphics and effective use of color.

• The solution is not complete indicating that parts of the problem are not understood.

• The solution addresses some, but not all of the mathematical components presented in the task.

• The student uses a strategy that is partially useful, and demonstrates some evidence of mathematical reasoning.

• Some parts of the project may be correct, but major errors are noted and the student could not completely carry out mathematical procedures.

• Your project is hard to follow because the material is presented in a manner that jumps around between unconnected topics.

• There is some use of appropriate mathematical representation.

• There is some use of mathematical terminology and notation appropriate for the problem.

• Your project contains low quality graphics and colors that do not add interest to the project.

• There is no solution, or the solution has no relationship to the task.

• No evidence of a strategy, procedure, or mathematical reasoning and/or uses a strategy that does not help solve the problem.

• The solution addresses none of the mathematical components presented in the task.

• There were so many errors in mathematical procedures that the problem could not be solved.

• There is no explanation of the solution, the explanation cannot be understood or it is unrelated to the problem.

• There is no use, or inappropriate use, of mathematical representations (e.g. figures, diagrams, graphs, tables, etc.).

• There is no use, or mostly inappropriate use, of mathematical terminology and notation.

• Your project is missing graphics and uses little to no color.

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The NROC Project 2019