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3.6 Equations and Problem Solving Date: ______________

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Steps to Solve Word Problems Identify the unknowns – Use variables Draw a diagram that will help you understand the problem Determine the formulas, equations that the problem is dealing with – Might be more than one Read a sentence at a time and make an equation

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The width of a rectangle is 3 in. less than its length. The perimeter of the rectangle is 26 in. What is the width of the rectangle. Examples Perimeter Formula: P = 2w + 2l w = l - 3 P = = 2(l – 3) + 2l 26 = 2l – 6 + 2l 26 = 4l – 6 32 = 4l 8 = l w = w = 5 in Let l = length Let w = width

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Examples Consecutive – in a row, back to back Let n = 1 st number n + 1 = 2 nd number n + 2 = 3 rd number n + n n + 2 = 72 3n + 3 = 72 3n = 69 n = , 24, 25 The sum of three consecutive integers is 72. Find the integers

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Examples JetRateTime Distance Traveled 1 st 2 nd Let t = time the 1 st plane travels t t – 1 180t 330(t – 1) 180t = 330(t – 1) 180t = 330t – t -150t = -330 t = 2.2 t – 1 = time the 2 nd jet travels An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left 1 hour later. The jet follows the same route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane?

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Examples HillRateTimeDistance Up Down Suppose you hike up a hill at 4 km/h. You hike back down at 6 km/h. Your hiking trip took 3 hours. How much time did it take you to hike up the hill? 4 6 Let t = time you go up the hill Let 3 – t = time you go down the hill t 3 – t 4t 6(3 – t) 4t = 6(3 – t) 4t = 18 – 6t + 6t 10t = t = 1.8 h

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