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Sec 1.5 Use Problem Solving Strategies and Models
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Goals
nGoal 1: To use a general proble= m solving plan to solve real-life problems.
nGoal 2: To use other problem solving strategies
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Problem Solving
<= span class=3DBB style=3D'position:absolute;left:-4.02%;top:.61em'>nOne o= f the major goals of this course is to learn how to use algeb= ra to solve real-life problems.  We have done some of this in previous lessons and will gain more experience in this section.
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Vocabulary
nUse a verbal model to write an equation in words before using mathematical symbols.
nExamples of problem-solving strategies, you might use to come up with a verbal = model are: using a formula, looking for a pattern, or drawing a diagram.
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Vocabulary
nNext assign labels to the verbal model you just created.
nCombine the two steps above to cre= ate a(n) algebraic model.
nFinally, solve the problem and ans= wer the question(s) asked.
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Example 1
nThe Bullet Train runs between the Japanese = cities of Osaka and Fukuoka, a distance of = 550 kilometers.&n= bsp; When it makes no stops, it takes 2 hours and 15 minutes to make the trip.  What is the average speed of the = train?
nFirst, create a verbal model then label:
<= span style=3D'visibility:hidden'>n
Distance
Rate
Time
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Example 1
nThe Bullet Train r= uns between the Japanese citie= s of Osaka and Fukuoka, a distance of 550 kilometers.  When it makes no stops, it takes 2 hours an= d 15 minutes to make the trip.=   What is the average speed of the = train?
<= span style=3D'font-size:88%'>nCombine the two fo= r an algebraic model.
<= span class=3DB1B style=3D'position:absolute;left:-4.26%;top:.74em'>n550 = =3D r (2.25)
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Example 1
<= span style=3D'font-size:75%'>nThe Bullet Train r= uns between the Japanese cities of Osaka and Fukuoka, a distance of 550 kilometers.  When it makes no stops, it takes 2 hours and 15 minutes to make the trip.  What is the average speed of the train?
<= span style=3D'font-size:75%'>nFinally, solve for= the rate. =
<= span class=3DB1B style=3D'position:absolute;left:-4.3%;top:.74em'>n550 = =3D r (2.25)
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Example 1
nThe Bullet Train runs between the Japanese cities = of Osaka and Fukuoka, a distance of 550 kilometers.  When it makes no stops, it takes 2 hours and 15 minutes to make the trip.  What is the average speed of the train?
<= span style=3D'font-size:75%'>nUnit analysis:
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Example 2
nParamotoring=   A paramotor is a parachute propelled by a fanlike motor.  The table shows the height h of a paramotorist t min= utes after beginning a descent.&nbs= p; Find the height of the paramotorist after seven minutes.
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Example 2
nIn this example,= we want to look for a pattern.  We can then use the pattern to write a verbal model for the height