Section 2.6 Percent, Rate, and Mixture Problems 159 b. Todd needs to make 4 gal of a 40% antifreeze solution for his truck. How much pure antifreeze and how much water should he mix together to get 4 gal of a 40% antifreeze solution? c. The Nut Company mixes pecans that sell for $8.25 per pound and walnuts that sell for $6.45 per pound to make 50 lb of a mixture that sells for $7.15 per pound. How much of each kind of nut should be put in the mixture? Distance Problems As illustrated in Section 2.5, Example 1c, distance traveled depends on one’s speed and the time traveled. Property: Distance Formula Distance = rate × time or d = rt Distance is measured in miles, feet, kilometers, and the like. Rate is measured in miles per hour, feet per second, kilometers per hour, and the like. Time is measured in hours, minutes, seconds, and the like. We can use this formula to determine how far a car travels if it is driven at a speed of 65 mph for 2 hr. d = (65 mph)(2 hr) = 130 mi For these word problems, there will be two people/things that are traveling. So, there will be two distances, rates, and times. One of these quantities will be given for each people/things. The other quantity will be unknown. The remaining quantity will be obtained using the distance formula. It is helpful to organize the information in a chart. Objective 4 Examples Use the distance formula to write an equation that will solve each problem. Solve the equation and answer the question using a complete sentence. 4a. Tatiana and Blair live 390 mi apart. They leave their homes at the same time and drive towards one another until they meet. Tatiana is traveling at 60 mph and Blair is traveling at 70 mph. How long will they drive until they meet one another? Solution 4a. What is unknown? The time that Tatiana and Blair travel is unknown. Since they leave at the same time and travel until they meet, their times are the same. Let t = the time Tatiana and Blair travel. What is known? They live 390 mi apart. Tatiana travels at a rate of 60 mph. Blair travels at a rate of 70 mph. Rate × Time = Distance Tatiana 60 t 60t Blair 70 t 70t 70t 390 miles 60t lair atiana Objective 4 ▶ Solve distance, rate, and time applications.
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