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1.5 Problem Solving Using Algebraic Models

1.5 Problem Solving Using Algebraic Models. Rates : the key word is per time– get some examples: mph, gallon per minute , doughnuts made per hour Be able to use a problem solving plan write a verbal model assign labels write an algebraic model solve the algebraic model answer the question.

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1.5 Problem Solving Using Algebraic Models

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  1. 1.5 Problem Solving Using Algebraic Models

  2. Rates: the key word is per time– get some examples: mph, gallon per minute, doughnuts made per hour • Be able to use a problem solving plan • write a verbal model • assign labels • write an algebraic model • solve the algebraic model • answer the question

  3. Examples a. On August 15, 1995 the Concorde flew 35,035 miles from New York City to New York City in 31 hours and 27 minutes. What was the average speed? b. Concorde flies at a rate of 1114 mph, how long will it take to fly 3,469 miles from New York City to London? c. A shower head advertises a maximum flow rate of 2.5 gallons per minute. Find the flow rate if it fills a 22 gallon bathtub in 9.5 minutes. Is this within the advertised limit?

  4. Common Formulas Unit analysis – making sure the units follow the mathematical correctly Example 2: a. Convert 20 feet to inches b. Convert 158 seconds to minutes c. Convert 920 feet per minute to mph d. 700 ft/min to miles/hour

  5. e. How far do you travel if going at the rate of 1114 miles per hour for 3.5 hours? f. You drove 280 miles, using 15 gallons of gasoline that cost $1.15 per gallon. If you get 24mi/gal on the highway and 16 in the city, how much did you spend for fuel for highway driving and how much for city driving? Total miles = 280 Fuel efficiency (highway) = 24 Amount of gas (highway) = x Fuel efficiency (city) = 16 Amount of gas (city) = 15 – x Total miles = fuel efficiency (hwy) x amt. gas + fuel efficiency (city) x amt. gas

  6. g. A fire truck is called to a scene. Three minutes later, a second truck is called. The first truck averages only 30 mph, but the second averages 60 mph. The trucks travel a total of 12 miles and arrive at the same time. How long from the first call did the trucks take to arrive? How far did each travel? We must first remember to change miles per hour to miles per minute.

  7. h. The table gives the heights from the floor to the first few steps of a flight of stairs. Determine the height of the 14th step. To do this we must look for a pattern. Height to top of a story = h Height of landing = 4 Height per story = 8 Story number = n Height to top of story = height of landing + height per story x story number We will substitute 15 in for n.

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