Solve the equation. ANSWER 62.4 ANSWER 17 ANSWER 11 Warm-Up Exercises 1. = r = 25+ 9x9x g = 636 () g – 18

ANSWER 497 ft Warm-Up Exercises 4. A balloon is released from a height of 5 feet above the ground. Its altitude (in feet) after t minutes is given by the expression. What is the altitude of the balloon after 6 minutes? 82t + 5

Example 1 Write and Use a Formula Chairlifts Chairlifts transport snowboarders and skiers to the tops of the ski runs. The Iron Horse Quad Chairlift in Montana carries skiers a distance of 3250 feet. The chairlift moves at a speed of 450 feet per minute. Find the time it takes the chairlift to travel the entire distance. SOLUTION You can use the formula to write a verbal model. rtd = VERBAL MODEL Time Rate = Distance

Example 1 Write and Use a Formula LABELSDistance(feet) Rate(feet per minute) Time(minutes) = = = t ALGEBRAIC MODEL = t Write algebraic model = t Divide each side by t ≈ Use a calculator. ANSWER It takes the chairlift about 7 minutes to travel the entire distance.

Checkpoint 1.Find the time it takes the chairlift in Example 1 to travel 1800 feet. ANSWER 4 min Write and Use a Formula

Write and Use an Algebraic Model Example 2 Conservation Low-flow faucets help conserve water. They have a flow rate of at most 2.5 gallons per minute. To test whether a faucet meets this standard, you time how long the faucet takes to fill a 1 -gallon container. The result is 0.3 minute. Find the flow rate for the faucet. Is it a low-flow faucet? SOLUTION VERBAL MODEL Volume of container Time needed to fill container Flow rate of faucet =

Write and Use an Algebraic Model Example 2 Volume of container 1 = (gallon) Flow rate of faucet r = (gallons per minute) Time needed to fill container 0.3 = (minute) LABELS 3.3r ≈ Divide each side by 0.3 ; use a calculator. ANSWER The flow rate is about 3.3 gallons per minute, which is greater than the standard for low-flow faucets. This is not a low-flow faucet. ALGEBRAIC MODEL Write algebraic model. () 0.31 = r

Look for a Pattern Example 3 Skyscrapers The table below gives the heights from the ground to the top of the first few stories of the Republic Plaza in Denver, Colorado. Determine the height from the ground to the top of the 9th story. SOLUTION Look at the difference in the heights given in the table. After the lobby, the height increases by 12.5 feet per story. You can use the observed pattern to write a model for the height. Height to top of story (ft) StoryLobby 36 2

Look for a Pattern Example 3 VERBAL MODEL Height of lobby Height of story Number of stories above lobby Height to top of a story =+ (feet) (feet per story) (stories) LABELS Height to top of a story h = Height of story 12.5 = Number of stories above lobby n = Height of lobby 36 = (feet)

Look for a Pattern Example 3 ANSWER The height to the top of the 9th story is about 136 feet. ALGEBRAIC MODEL 12.5n = 36h + Write algebraic model = 36h + () 8 Substitute for n. = – = 136h Simplify.

Draw a Diagram Example 4 Railroads In 1862, two companies were given the rights to build a railroad from Omaha, Nebraska, to Sacramento, California. The Central Pacific Railroad began from Sacramento in late Twenty months later, the Union Pacific Railroad began from Omaha. The Central Pacific Railroad averaged 10.5 miles of track per month. The Union Pacific Railroad averaged 23.6 miles of track per month. The illustration shows the two companies meeting in Promontory Summit, Utah, as the 1780 miles of track were completed. When did the companies meet? How many miles of track did each company build?

Draw a Diagram Example 4 SOLUTION Begin by drawing and labeling a diagram, as shown. SacramentoPromontory SummitOmaha VERBAL MODEL Total miles of track Union Pacific rate Central Pacific time Union Pacific time =+ Central Pacific rate

Draw a Diagram Example 4 LABELS Total miles of track 1780 = (miles) (months) Central Pacific time t = Central Pacific rate 10.5 = (miles per month) Union Pacific rate 23.6 = (miles per month) Union Pacific time t 20 = – (months) ALGEBRAIC MODEL Write algebraic model. 10.5t = () 20t – Simplify. 34.1t = t = t – Distributive property 34.1t = – Combine like terms.

Draw a Diagram Example 4 66t ≈ Divide each side by ANSWER The construction took 66 months from the time the Central Pacific Railroad began in So, the companies met in early The number of miles of track built by each company is: years Central Pacific: = 10.5 miles month 66 months 693 miles 23.6 miles month months 1086 miles () 2066 – ≈ Union Pacific:

2.You borrow $195 from your aunt. Your aunt is not charging you any interest, but you want to repay her as soon as possible. You can afford to pay her $15 per week. Use the problem solving plan to find how long it will take you to repay your aunt. Checkpoint ANSWER 13 wk Write and Use a Simple Model