2.1 Using Problem Solving Strategies and Models

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2.1 Using Problem Solving Strategies and Models Goal : Solve problems using verbal models Pg. 24

Vocabulary Verbal Model Distance Formula Writing an equation in words before you write it in mathematical symbols Distance Formula Distance = rate · time

Example #1, (Use a formula) A bus travels at an average rate of 50 miles per hour. The distance between Atlanta and Miami is 663 miles. How long would it take for the bus to travel from Atlanta to Miami? Solution Use the distance formula for distance traveled as a verbal model. = · ________ = ________ · t An equation for this situation is _____ = _____t. _____ = _____t (Write the equation) _____ ≈ t (Divide each side by _____) Distance (miles) Rate (mi/h) Time (hours)

Continued The amount of time it would take to travel from Atlanta to Miami is about ______ hours. Use unit analysis to check your answer _____ miles ≈ _____ miles · _____ hours hours

Checkpoint In Example 1, how fast is the buss traveling if it takes 22 hours to travel from San Francisco to Colorado Springs, a distance of 1335 miles? ≈ 60.7 miles per hour

Example #2, (Look for a pattern) The table shows the height (h) of a jet airplane (t) minutes after beginning its descent. Find the height of the airplane after 9 minutes. Solution The height decreases by 3000 feet per minute. You can use this equation to write a verbal model for the height. Time (min), t 1 2 3 4 Height (ft), h 35,000 32,000 29,000 26,000 23,000

Solution Height = Initial Height – Rate of Descent · Time This is a Linear Equation So, the height after 9 minutes is h = ________ - _________(___) = ________ feet

Class Work and Homework Pg. 26, 1 – 17 all