Step 5: Check the answer, and interpret the solution as it relates to the problem. The pharmacist needs 150 mL of the 8% solution and 50 mL of the 16% solution. Check the answers in the original problem to verify that they are correct. YOU TRY 4 Write an equation, and solve. How many milliliters of a 5% acid solution and how many milliliters of a 17% acid solution must be mixed to obtain 60 mL of a 13% acid solution? 5 Solve Distance, Rate, and Time Problems EXAMPLE 5 In-Class Example 5 Bart and Homer leave home on their bikes going in opposite directions. Bart pedals 2 mph faster than Homer, and after 1.5 hours they are 21 miles apart. Find each of their speeds. Answer: Bart: 8 mph; Homer: 6 mph Sketch a picture to visualize distance, rate, and time problems. Write an equation, and solve. Two cars leave Kearney, Nebraska, one driving east and the other heading west. The eastbound car travels 4 mph faster than the westbound car, and after 2.5 hours they are 330 miles apart. Find the speed of each car. Solution Step 1: Read the problem carefully, and identify what we are being asked to fi nd. We must fi nd the speed of the eastbound and westbound cars. We will draw a picture to help us see what is happening in this problem. After 2.5 hours, the positions of the cars look like this: Kearney West East 2.5x 2.5y 330 miles Step 2: Choose variables to represent the unknown quantities. x the speed of the westbound car y the speed of the eastbound car Step 3: Write a system of equations using two variables. Let’s make a table using the equation d rt. Fill in the time, 2.5 hr, and the rates fi rst, then multiply those together to fi ll in the values for the distance. d r t Westbound 2.5x x 2.5 Eastbound 2.5y y 2.5 Label the picture with the expressions for the distances. To get one equation, look at the picture and think about the distance between the cars after 2.5 hr. English: Distance traveled by westbound car plus Distance traveled by eastbound car equals Distance between them T T T T T Equation: 2.5x 2.5y 330 The equation is 2.5x 2.5y 330. 280 CHAPTER 4 Linear Equations and Inequalities in Two Variables www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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