How Fast to Drive

HOW FAST TO DRIVE?

Enduring Understanding: Develop a better understanding of how to use rates to construct a solution to a problem situation and how using minimum and maximum values is not always the best solution.

Essential Questions:

 How can information be analyzed to draw a conclusion?  How is a conclusion supported by mathematical information?  How is a plan formulated to analyze the given information?  How is a solution determined to be viable?

Lesson Overview:

 Before allowing the students the opportunity to start the activity: access their prior knowledge regarding what is meant by miles per gallon and how that is used to determine the miles a vehicle can travel on a tank of gas, talk about trips they have taken. Did they concern themselves with gas usage or miles per gallon? Is it an issue today with getting optimal miles per gallon?  What is meant by the terms minimum and maximum? Do we always strive to attain the minimum or maximum? When are the minimums or maximums not the best solution to a situation?  A good warm-up would be the Express Train.  How is a problem situation decoded so that a person understands what is being asked?  What mathematical information should be used to support a particular conclusion?  How will the students make their thinking visible?  Use resources from your building.  This problem was written when $2.10 was an accurate cost per gallon for gasoline. You may want to adjust the price to match what is relevant when you use this activity or have the students use $2.10, then use the present day cost. A discussion could ensue regarding the influence of the price per gallon on out of pocket expenses that would need to be recovered by shipping companies. Who really pays for those increases?

EALRs/GLEs

2.2.2 3.2.2 3.3.1

Item Specifications: SR02; SR05

Assessment:

 Use WASL format items that link to what is being covered by the classroom activity  Include multiple choice questions How Fast To Drive?

You are the president of a trucking service that transports food long distances on the interstate freeways. You pay your drivers by the hour, so you want them to make the trips as fast as possible. On the other hand, you know that your trucks get worse gas mileage (they go fewer miles per gallon) if you drive at speeds greater than 50 miles per hour. You are trying to find the speed to recommend to the drivers so that the total cost of the trip is as low as possible.

Information you have collected: - The trip is 800 miles long and is made virtually non-stop because you have two drivers in the truck. - The road has speed limits of 50 mph minimum and 70 mph maximum (under normal conditions.) - Gas costs $2.10 a gallon. - The two drivers together cost $120 per hour, including benefits. - Trucks get 11 miles per gallon if they go 50 miles per hour. - For every 5 miles per hour over 50 miles per hour, the trucks lose 2 miles per gallon.

1. Predict why going the maximum speed limit might NOT be the most economical speed.

______

2. Predict why going the minimum speed limit might NOT be the most economical speed.

______

______3. Fill in the cost chart below.

Show clearly how you find the cost in each part of the chart.

SPEED DRIVER COST GAS COST TOTAL COST (MPH) 50

Use the work shown in the chart to answer the following questions.

4. Describe in words how you will find the driver cost for a trip at a particular speed S.

______

______5. Describe in words how you will find the gas cost for a trip at a particular speed S.

______

6. What speed should your trucks be driven in order to have the lowest overall possible cost? Explain your answer.

______

______7. A car made a trip of 352 miles on 16.8 gallons of gasoline.

Which is closest to the number of miles per gallon the car got on that trip?

O A. 10 mpg O B. 20 mpg O C. 30 mpg O D. 40 mpg

8. John and Bill drove their truck to California. John drove for three straight hours averaging 55 mph. Bill then took over the driving for four straight hours averaging 65 mph. They continued this pattern until they covered 2125 miles.

Which represents the number of hours to complete the trip?

O A. 14 O B. 35 O C. 44 O D. 60

9. A flower shop delivery van traveled these distances during one week:

Monday--104.1 miles Tuesday--117.8 miles Wednesday--92.3 miles Thursday--168.7 miles Friday--225.6 miles.

How many gallons of gas were used by the delivery van during this week?

What other information is needed in order to answer this question?

O A. The average speed traveled in miles per hour O B. The cost of gasoline per gallon O C. The average number of miles per gallon for the van O D. The number of different deliveries the van made

10. Two automobiles with different fuel efficiencies both travel 12,000 miles per year. Car A averages 40 miles per gallon and Cab B averages 24 miles per gallon.

Which represents how many fewer gallons of gasoline Car A would require per year?

O A. 200 O B. 300 O C. 500 O D. 750