2. EXAMPLE 1 Use a formula High-speed Train The Acela train travels between Boston and Washington, a distance of 457 miles. The trip takes 6.5 hours. What is the average speed? SOLUTION You can use the formula for distance traveled as a verbal model. 457 = r 6.5 Distance (miles) = Rate (miles/hour) Time (hours)

3. EXAMPLE 1 Use a formula An equation for this situation is 457 = 6.5r. Solve for r. 457 = 6.5r 70.3r Write equation. Divide each side by 6.5. The average speed of the train is about 70.3 miles per hour. ANSWER You can use unit analysis to check your answer. 457 miles 6.5 hours 70.3 miles 1 hour CHECK

4. GUIDED PRACTICE for Example 1 1. AVIATION: A jet flies at an average speed of 540 miles per hour. How long will it take to fly from New York to Tokyo, a distance of 6760 miles? Jet takes about 12.5 hours to fly from New York to Tokyo. ANSWER

5. EXAMPLE 2 Look for a pattern Paramotoring A paramotor is a parachute propelled by a fan-like motor. The table shows the height h of a paramotorist t minutes after beginning a descent. Find the height of the paramotorist after 7 minutes.

6. EXAMPLE 2 Look for a pattern SOLUTION The height decreases by 250 feet per minute. You can use this pattern to write a verbal model for the height. An equation for the height is h = 2000 – 250t.

7. EXAMPLE 2 Look for a pattern So, the height after 7 minutes is h = 2000 – 250(7) = 250 feet. ANSWER

8. EXAMPLE 3 Draw a diagram Banners You are hanging four championship banners on a wall in your school’s gym. The banners are 8 feet wide. The wall is 62 feet long. There should be an equal amount of space between the ends of the wall and the banners, and between each pair of banners. How far apart should the banners be placed? SOLUTION Begin by drawing and labeling a diagram, as shown below.

9. EXAMPLE 3 Draw a diagram From the diagram, you can write and solve an equation to find x. x + 8 + x + 8 + x + 8 + x + 8 + x = 62 5x + 32 = 62 Subtract 32 from each side. 5x5x = 30 x=6 Divide each side by 5. Combine like terms. Write equation. The banners should be placed 6 feet apart. ANSWER

10. EXAMPLE 4 Standardized Test Practice SOLUTION STEP 1 Write a verbal model. Then write an equation. An equation for the situation is 460 = 30g + 25(16 – g).

11. EXAMPLE 4 Standardized Test Practice Solve for g to find the number of gallons used on the highway. STEP 2 460 = 30g + 25(16 – g) 460 = 30g + 400 – 25g 460 = 5g + 400 60 = 5g 12 = g Write equation. Distributive property Combine like terms. Subtract 400 from each side. Divide each side by 5. The car used 12 gallons on the highway. ANSWER The correct answer is B. CHECK: 30 12 + 25(16 – 12) = 360 + 100= 460

12. GUIDED PRACTICE for Examples 2, 3 and 4 2. PARAMOTORING: The table shows the height h of a paramotorist after t minutes. Find the height of the paramotorist after 8 minutes. So, the height after 8 minutes is h = 2400 – 210(8) = 720 ft ANSWER

13. GUIDED PRACTICE for Examples 2, 3 and 4 3. WHAT IF? In Example 3, how would your answer change if there were only three championship banners? The space between the banner and walls and between each pair of banners would increase to 9.5 feet. ANSWER

14. GUIDED PRACTICE for Examples 2, 3 and 4 4. FUEL EFFICIENCY A truck used 28 gallons of gasoline and traveled a total distance of 428 miles. The truck’s fuel efficiency is 16 miles per gallon on the highway and 12 miles per gallon in the city. How many gallons of gasoline were used in the city? Five gallons of gas were used. ANSWER