1. Financial Algebra © Cengage/South-Western Slide 1 AUTOMOBILE OWNERSHIP 5-1Classified Ads 5-2Buy or Sell a Car 5-3Graph Frequency Distributions 5-4Automobile Insurance 5-5Linear Automobile Depreciation 5

2. Financial Algebra © Cengage/South-Western Slide 2 AUTOMOBILE OWNERSHIP 5-6Historical and Exponential Depreciation 5-7Driving Data 5-8Driving Safety Data 5-9Accident Investigation Data 5

3. Financial Algebra © Cengage/South-Western Slide 3 5-8 DRIVING SAFETY DATA Calculate reaction time and distance in the English Standard System. Calculate and use the braking distance in both the English Standard and Metric Systems. Calculate and use the total stopping distance in both the English Standard and Metric Systems. OBJECTIVES

4. Financial Algebra © Cengage Learning/South-Western Slide 4 reaction time thinking time reaction distance braking distance total stopping distance Key Terms

5. Financial Algebra © Cengage Learning/South-Western Slide 5 How can you use mathematics to become a safer driver? How long do you think it takes a driver to react to something in the roadway that requires the car to stop? When a driver applies the brakes to a car How long does it take the car to stop? What distance does the car travel before it stops?

6. Financial Algebra © Cengage Learning/South-Western Slide 6 Example 1 What is the reaction distance for a car traveling approximately 48 miles per hour? Prove this solution: reaction distance = 1.5 feet per second

7. Financial Algebra © Cengage Learning/South-Western Slide 7 Example 1 What is the reaction distance for a car traveling approximately 48 miles per hour? Prove this solution: reaction distance = 1.5 feet per second

8. Financial Algebra © Cengage Learning/South-Western Slide 8 Example 1 reaction distance = 1.5 feet per second 55 mph = miles 1 hour 55 mph * #hours = 55 * 1 =55 miles 1 hour#minutes1(60 min * 60 sec)3600 sec 55 miles = 55 mile * 5280 feet = 290,400 = 80.667 ≈81 ft/sec. 3600 sec3600 sec3600

9. Financial Algebra © Cengage Learning/South-Western Slide 9 Example 1 55 mph = 81 ft/sec. 0.75 * 81 ft/sec. = 60.75 ft. 1.5 * 81 ft./sec = 121.5 ft.* NOTE: a profession basketball court is 94 feet long a high school basketball court is 84 feet long

10. Financial Algebra © Cengage Learning/South-Western Slide 10 Example 1 What is the reaction distance for a car traveling approximately 48 miles per hour? Mph * 5280 ft. = x ft./sec 3600 sec 48 * 5280 = 253,440 = 70.4 feet3600

11. Financial Algebra © Cengage Learning/South-Western Slide 11 A car is traveling at 65 mi/h. Approximately how far will it travel during the average reaction time? Mph * 5280 ft. = x ft./sec 3600 sec 65 * 5280 = 343,200 = 95.33 feet3600 CHECK YOUR UNDERSTANDING

12. Financial Algebra © Cengage Learning/South-Western Slide 12 #2 #3 #4 #5 #6 #7 Applications, p.270

13. Financial Algebra © Cengage Learning/South-Western Slide 13 Example 2 What is the approximate braking distance for a car traveling at 48 mi/h? Use the braking distance formula s 2 / 20 Type into your calculator: 48 ^2 ÷ 20 = = 115.2

14. Financial Algebra © Cengage Learning/South-Western Slide 14 What factors also need to be taken into account that might add to or subtract from the braking distance? CHECK YOUR UNDERSTANDING

15. Financial Algebra © Cengage Learning/South-Western Slide 15 #8 #9 #10 Applications, p.270

16. Financial Algebra © Cengage Learning/South-Western Slide 16 EXAMPLE 3 Rachel is driving at 48 mi/h on a one-lane highway. She sees an accident directly ahead of her about 200 feet away. Will she be able to stop in time?

17. Financial Algebra © Cengage Learning/South-Western Slide 17 What is the total stopping distance for a car traveling at 65 mi/h? CHECK YOUR UNDERSTANDING

18. Financial Algebra © Cengage Learning/South-Western Slide 18 #11 #12 Applications, p.270

19. Financial Algebra © Cengage Learning/South-Western Slide 19 EXAMPLE 4 Desireé is traveling through Canada. The speedometer in her rented car indicates kilometers per hour and all of the road signs give distances in kilometers. She knows that one kilometer is equal to 1,000 meters and one meter is a little more than 3 feet. Determine Desireé’s total stopping distance if she is traveling 88 kilometers per hour.

20. Financial Algebra © Cengage Learning/South-Western Slide 20 A car is traveling at 78 km/h. What is the total stopping distance in meters? Round your answer to the nearest hundredth of a meter. CHECK YOUR UNDERSTANDING

21. Financial Algebra © Cengage Learning/South-Western Slide 21 Toni’s car is traveling 75 km/h. Randy’s car is behind Toni’s car and is traveling 72 km/h. Toni notices a family of ducks crossing the road 50 meters ahead of her. Will she be able to stop before she reaches the ducks? What is the least distance that Randy’s car can be from Toni’s car to avoid hitting her car, if he reacts as soon as he sees her brakes? EXTEND YOUR UNDERSTANDING