Unit 3 Project 5: Running for the Gold During the 1992 and 1996 Olympic Games, Gail Deevers of the United States won the gold medal for finishing first in the 100-meter run. She ran at an average speed of about 9 meters per second Go to part a to begin. Time (seconds) 0 Distance Calcnlation Distance (meters) 0 2 9-2 18 4 6 BO 10 Using her average speed, complete the table above to show Gail's distance in meters every two seconds during a 100-meter run. b. Lett be the run time and G be Gail's distance from the official start line. Follow the pattern in column two and write the equation that gives Gin terms of t c. Suppose Paul is able to maintain an average speed of 5 meters per second during a short run. If Paul is given a 40-meter head start, let's see how he will do competing in a 100- meter race against Gail. Complete the table below where Paul begins the race 40 meters ahead of the official starting line. 40+5:2 Time (seconds) 0 Distance Calculation Distance (meters) 40 2 50 4 6 8 10 2 Lett be the race time and Pbe Paul's distance from the official start line. Follow the pattem in the table above to find an equation that gives P in terms of r. . Use the information from the two tables to find the time and distance when Gail catches up with Paul during their 100-meter race. f. Who wins the race? Explain your reasoning. 8. Assuming both runners maintained their constant speed, set up and solve an equation that will give you the winning time. Round the time to the nearest tenth of a second. 1. How far ahead was the winner when he or she crossed the finish line? Round the distance to the nearest tenth of a meter. Assuming both runners maintained their constant speed, set up and solve an equation that will give the time the second place runner crossed the finish line, Part 2: Suppose a third runner named Catia runs in a 100-meter race with Gail and Paul The equation below represents her distance in meters from the starting line in terms of time in seconds. C=30+67 j In what time does Catia finish the race? Round to the nearest tenth of a second. k List the order in which the three rumers finish the race. | Find an equation that represents the distance in terms of timer for another runner, called The Dude, who want to race against Gail, Paul, and Catia. Create the equation so that The Dude begins the 100-meter race at the official starting line and is guaranteed to win this 100-meter race. Use the variable D to represent The Dude's distance in meters from the start line. Be sure the runner's speed is within a human's physical limits. m. Find an equation that represents another runner whose average speed is 4 meters per second, has a head start that begins less than 3/4 of the 100 meter distance, and is guaranteed to win a 100-meter race against all the others. Name this last runner and 2 explain why this person will win the race. Unit 3 Project 6: Signing the Best Contract Suppose that Megan wrote a TOTICE novel during her last year in school, and two publishers extend her offers to sign the manuscript for publication Company A offers her a $10,000 signs on boms and 15% of the book's total saler Company B offers her 2 35,000 sign-un baromes and 18% of the book's total sales. Assuming both companies would spend at out the same amount on advertising and promoting the book, which publisher should she sign with? Go to part a e Complete the following table to see how Megan's book income depends on total sales. Tatil Sales Income from Income from Company A ($) Company B (9) 30 25,000 50,000 75,000 100,000 125,000 150,000 175,000 200,000 b Describe the change in income of Company A and Company B as total sales increase. a Lett be the total sales in 5) and y be the income (in 5) that Negan would receive Using these variables, setup two equations for the incomes from Companies A and B. Hint the income y from each company is a fixed bonus plus a percent of total sales x. Company A: Company B. d. Based on the data in the table, estimate the total sales that will produce the same income from each company? Explain your reasoning e. To find the exact amount of total sales that will produce the same income from each company, set the expression on the right side of the equation of Company A equal to the expression on the right side of the equation for Company B, then solve this new equation. Round to the nearest dollar. Based on all of the information, how would you advise Megan on selecting a publisher? Be sure to support your advice with quantitative reasoning Unit 3 Project 7: Back to School Marissa is going back to school to get her teaching certificate She needs 12 adetitional credits to obtain certification and plans to attend one of the two local colleges City College costs $70 per credit plus a $150 one time registration fee, while State College costs $95 per credit and has no registration fee Assuming both colleges have a similar academic repdation, which is the better choice based on cost? Go to partato begin Show the computational steps necessary to find the cost of taking one 3-credit course at City College and repeat the process for one 4-credit couse at the same school Suppose the total number of credits a student takes is represented by the variable and the cost to attend City College is represented by the variable C Write a formanla that expresses the cost C in terms of the number of credits taken a Show the corriputational steps necessary to find the cost of taking one 3-credit course at State College and repeat the process for one 4-credit course at the same school . If the cost to attend State College is represented by S, then write a formula that expresses the cost S in terms of the number of credits taken 2 & Complete the table below that gives the total cost at each college, including registration fee, for taking from 3 to 12 credits. Number of Credits Cost at City College Cost af State College C (in $) Sin $) 3 4 5 6 7 8 9 10 11 12 f. If it costs Marissa's friend Megan $1130 to attend City College last semester, then how many credits did she take? Set up and solve the linear equation that will give the answer to this question Then verify your solution by extending the table you constructed in part e. g. Based on the data in the table, when does City College cost the same as State College? h. Answer the questions below. Over what range of credits does City College cost more than State College? . Over what range of credits does City College cost less than State College? Symbolically the cost at City College should be equal to the cost at State College when C-si Verify your answer to part g, by setting the right side expressions from the equations in parts b and d equal to each other and then solve for n