Computing Average Speed In going from Chicago to Atlanta,

The process of using variables to represent unknown quantities and then finding relationships that involve these variables is referred to as

The money paid for the use of money is

Objects that move at a constant speed are said to be in

rue or False The amount charged for the use of principal for a given period of time is called the rate of interest.

True or False If an object moves at an average speed the distance d covered in time t is given by the formulad = rt. r

Suppose that you want to mix two coffees in order to obtain 100 pounds of a blend.If x represents the number of pounds of coffee A, write an algebraic expression that represents the number of pounds of coffee B.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Geometry The area of a circle is the product of the number and the square of the radius.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Geometry The circumference of a circle is the product of the number and twice the radius.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Geometry The area of a square is the square of the length of a side.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Geometry The perimeter of a square is four times the length of a side.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Physics Force equals the product of mass and acceleration

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Physics Pressure is force per unit area.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Physics Work equals force times distance.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Physics Kinetic energy is one-half the product of the mass and the square of the velocity.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Business The total variable cost of manufacturing x dishwashers is $150 per dishwasher times the number of dishwashers manufactured.

In Problems 716, translate each sentence into a mathematical equation. Be sure to identify the meaning of all symbols.Business The total revenue derived from selling x dishwashers is $250 per dishwasher times the number of dishwashers sold.

Financial Planning Betsy, a recent retiree, requires $6000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% per year. How much money should be invested in each to realize exactly $6000 in interest per year?

Financial Planning After 2 years, Betsy (see Problem 17) finds that she will now require $7000 per year. Assuming that the remaining information is the same, how should the money be reinvested?

Banking A bank loaned out $12,000, part of it at the rate of 8% per year and the rest at the rate of 18% per year.If the interest received totaled $1000, how much was loaned at 8%?

Banking Wendy, a loan officer at a bank, has $1,000,000 to lend and is required to obtain an average return of 18% per year.If she can lend at the rate of 19% or at the rate of 16%, how much can she lend at the 16% rate and still meet her requirement?

Blending Teas The manager of a store that specializes in selling tea decides to experiment with a new blend. She will mix some Earl Grey tea that sells for $5 per pound with some Orange Pekoe tea that sells for $3 per pound to get 100 pounds of the new blend. The selling price of the new blend is to be $4.50 per pound, and there is to be no difference in revenue from selling the new blend versus selling the other types. How many pounds of the Earl Grey tea and Orange Pekoe tea are required?

Business: Blending Coffee A coffee manufacturer wants to market a new blend of coffee that sells for $3.90 per pound by mixing two coffees that sell for $2.75 and $5 per pound,respectively.What amounts of each coffee should be blended to obtain the desired mixture? [Hint: Assume that the total weight of the desired blend is 100 pounds.]

Business: Mixing Nuts A nut store normally sells cashews for $9.00 per pound and almonds for $3.50 per pound. But at the end of the month the almonds had not sold well, so, in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for $7.50 per pound. How many pounds of cashews should be mixed with the almonds to ensure no change in the profit?

Business: Mixing Candy A candy store sells boxes of candy containing caramels and cremes. Each box sells for $12.50 and holds 30 pieces of candy (all pieces are the same size). If the caramels cost $0.25 to produce and the cremes cost $0.45 to produce, how many of each should be in a box to make a profit of $3?

Physics: Uniform Motion A motorboat can maintain a constant speed of 16 miles per hour relative to the water. The boat makes a trip upstream to a certain point in 20 minutes; the return trip takes 15 minutes. What is the speed of the current? See the figure.

Physics: Uniform Motion A motorboat heads upstream on a river that has a current of 3 miles per hour. The trip upstream takes 5 hours, and the return trip takes 2.5 hours.What is the speed of the motorboat? (Assume that the motorboat maintains a constant speed relative to the water.)

Physics: Uniform Motion A motorboat maintained a constant speed of 15 miles per hour relative to the water in going 10 miles upstream and then returning. The total time for the trip was 1.5 hours. Use this information to find the speed of the current.

Physics: Uniform Motion Two cars enter the Florida Turnpike at Commercial Boulevard at 8:00 AM, each heading for Wildwood. One cars average speed is 10 miles per hour more than the others. The faster car arrives at Wildwood at 11:00 AM, hour before the other car. What was the average speed of each car? How far did each travel?1 2

Moving Walkways The speed of a moving walkway is typically about 2.5 feet per second. Walking on such a moving walkway, it takes Karen a total of 40 seconds to travel 50 feet with the movement of the walkway and then back again against the movement of the walkway. What is Karens normal walking speed?

Moving Walkways The Gare Montparnasse train station in Paris has a high-speed version of a moving walkway.If he walks while riding this moving walkway, Jean Claude can travel 200 meters in 30 seconds less time than if he stands still on the moving walkway. If Jean Claude walks at a normal rate of 1.5 meters per second, what is the speed of the Gare Montparnasse walkway?

Tennis A regulation doubles tennis court has an area of 2808 square feet. If it is 6 feet longer than twice its width, determine the dimensions of the court. Source: United States Tennis Association

Laser Printers It takes an HP LaserJet 1300 laser printer 10 minutes longer to complete a 600-page print job by itself than it takes an HP LaserJet 2420 to complete the same job by itself. Together the two printers can complete the job in 12 minutes. How long does it take each printer to complete the print job alone? What is the speed of each printer?

Working Together on a Job Trent can deliver his newspapers in 30 minutes. It takes Lois 20 minutes to do the same route. How long would it take them to deliver the newspapers if they work together?

Working Together on a Job Patrice, by himself, can paint four rooms in 10 hours.If he hires April to help, they can do the same job together in 6 hours.If he lets April work alone, how long will it take her to paint four rooms?

Enclosing a Garden A gardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border 2 feet wide surrounding it. See the figure. (a) If the length of the garden is to be twice its width, what will be the dimensions of the garden? (b) What is the area of the garden? (c) If the length and width of the garden are to be the same, what would be the dimensions of the garden? (d) What would be the area of the square garden?

Construction A pond is enclosed by a wooden deck that is 3 feet wide.The fence surrounding the deck is 100 feet long. (a) If the pond is square, what are its dimensions? (b) If the pond is rectangular and the length of the pond is to be three times its width, what are its dimensions? (c) If the pond is circular, what is its diameter? (d) Which pond has the most area?

Football A tight end can run the 100-yard dash in 12 seconds. A defensive back can do it in 10 seconds. The tight end catches a pass at his own 20-yard line with the defensive back at the 15-yard line.(See the figure.) If no other players are nearby, at what yard line will the defensive back catch up to the tight end? [Hint: At time the defensive back is 5 yards behind the tight end.]

Computing Business Expense Therese, an outside salesperson, uses her car for both business and pleasure. Last year,she traveled 30,000 miles, using 900 gallons of gasoline. Her car gets 40 miles per gallon on the highway and 25 in the city. She can deduct all highway travel, but no city travel, on her taxes. How many miles should Therese be allowed as a business expense?

Mixing Water and Antifreeze How much water should be added to 1 gallon of pure antifreeze to obtain a solution that is 60% antifreeze?

Mixing Water and Antifreeze The cooling system of a certain foreign-made car has a capacity of 15 liters. If the system is filled with a mixture that is 40% antifreeze, how much of this mixture should be drained and replaced by pure antifreeze so that the system is filled with a solution that is 60% antifreeze?

Chemistry: Salt Solutions How much water must be evaporated from 32 ounces of a 4% salt solution to make a 6% salt solution?

Chemistry: Salt Solutions How much water must be evaporated from 240 gallons of a 3% salt solution to produce a 5% salt solution?

Purity of Gold The purity of gold is measured in karats, with pure gold being 24 karats. Other purities of gold are expressed as proportional parts of pure gold.Thus, 18-karat gold is or 75% pure gold; 12-karat gold is or 50% pure gold; and so on. How much 12-karat gold should be mixed with pure gold to obtain 60 grams of 16-karat gold?

Chemistry: Sugar Molecules A sugar molecule has twice as many atoms of hydrogen as it does oxygen and one more atom of carbon than oxygen. If a sugar molecule has a total of 45 atoms, how many are oxygen? How many are hydrogen?

Running a Race Mike can run the mile in 6 minutes, and Dan can run the mile in 9 minutes.If Mike gives Dan a head start of 1 minute, how far from the start will Mike pass Dan? How long does it take? See the figure.

Range of an Airplane An air rescue plane averages 300 miles per hour in still air. It carries enough fuel for 5 hours of flying time. If, upon takeoff, it encounters a head wind of how far can it fly and return safely? (Assume that the wind remains constant.)

Emptying Oil Tankers An oil tanker can be emptied by the main pump in 4 hours.An auxiliary pump can empty the tanker in 9 hours. If the main pump is started at 9 AM, when should the auxiliary pump be started so that the tanker is emptied by noon?

Cement Mix A 20-pound bag of Economy brand cement mix contains 25% cement and 75% sand. How much pure cement must be added to produce a cement mix that is 40% cement?

Emptying a Tub A bathroom tub will fill in 15 minutes with both faucets open and the stopper in place. With both faucets closed and the stopper removed, the tub will empty in 20 minutes. How long will it take for the tub to fill if both faucets are open and the stopper is removed?

Using Two Pumps A 5-horsepower (hp) pump can empty a pool in 5 hours.A smaller, 2-hp pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool.After two hours, the 2-hp pump breaks down. How long will it take the larger pump to empty the pool?

A Biathlon Suppose that you have entered an 87-mile biathlon that consists of a run and a bicycle race. Duringyour run, your average speed is 6 miles per hour, and during your bicycle race, your average speed is 25 miles per hour. You finish the race in 5 hours. What is the distance of the run? What is the distance of the bicycle race?

Cyclists Two cyclists leave a city at the same time, one going east and the other going west. The westbound cyclist bikes 5 mph faster than the eastbound cyclist. After 6 hours they are 246 miles apart. How fast is each cyclist riding?

Comparing Olympic Heroes In the 1984 Olympics, C.Lewis of the United States won the gold medal in the 100- meter race with a time of 9.99 seconds. In the 1896 Olympics,Thomas Burke, also of the United States, won the gold medal in the 100-meter race in 12.0 seconds.If they ran in the same race repeating their respective times, by how many meters would Lewis beat Burke?

Constructing a Coffee Can A 39-ounce can of Hills Bros. coffee requires 188.5 square inches of aluminum. If its height is 7 inches, what is its radius? [Hint:The surface area S of a right cylinder is where r is the radius and h is the height.]S = 2pr2 + 2prh,

Critical Thinking You are the manager of a clothing store and have just purchased 100 dress shirts for $20.00 each. After 1 month of selling the shirts at the regular price, you plan to have a sale giving 40% off the original selling price. However, you still want to make a profit of $4 on each shirt at the sale price.What should you price the shirts at initially to ensure this? If, instead of 40% off at the sale, you give 50% off, by how much is your profit reduced?

Critical Thinking Make up a word problem that requires solving a linear equation as part of itssolution.Exchange problems with a friend. Write a critique of your friends problem.

Critical Thinking Without solving, explain what is wrong with the following mixture problem: How many liters of 25% ethanol should be added to 20 liters of 48% ethanol to obtain a solution of 58% ethanol? Now go through an algebraic solution.What happens?

Computing Average Speed In going from Chicago to Atlanta, a car averages 45 miles per hour, and in going from Atlanta to Miami, it averages 55 miles per hour.If Atlanta is halfway between Chicago and Miami, what is the average speed from Chicago to Miami? Discuss an intuitive solution. Write a paragraph defending your intuitive solution. Then solve the problem algebraically. Is your intuitive solution the same as the algebraic one? If not, find the flaw.

Speed of a Plane On a recent flight from Phoenix to Kansas City, a distance of 919 nautical miles, the plane arrived 20 minutes early. On leaving the aircraft, I asked the captain, What was our tail wind? He replied, I dont know, but our ground speed was 550 knots. How can you determine if enough information is provided to find the tail wind? If possible, find the tail wind. (1 knot = 1 nautical mile per hour)