160 Chapter 2 Linear Equations and Inequalities Solving an Application Involving Distance, Rate, and Time Two families that live 270 mi apart plan to meet for an afternoon picnic at a park that is located between their two homes. Both families leave at 9.00 A.M., but one family averages 12 mph faster than the other family. If the families meet at the designated spot 212 hr later, determine a. The average rate of speed for each family. b. The distance each family traveled to the picnic. Solution: For simplicity, we will call the two families, Family A and Family B. Let Family A be the family that travels at the slower rate (Figure 2-9). Example 4 270 miles Step 1: Read the problem and draw a sketch. Family A Family B Figure 2-9 Let x represent the rate of Family A. Step 2: Label the variables. Then 1x 122 is the rate of Family B. Distance Rate Time 2.5x Family A x 2.5 Family B 2.51x 122 x 12 2.5 To complete the first column, we can use the relationship To set up an equation, recall that the total distance between the two families is given as 270 mi. Step 3: a total distance traveled by Family B Distance traveled by Family A ° ¢ ° b distance 270 Step 4: Write a mathematical equation. Step 5: Solve for x. ¢ 2.5x 2.51x 122 2.5x 2.51x 122 270 2.5x 2.5x 30 270 5.0x 30 270 5x 240 a. Family A traveled 48 mph. x 48 Family B traveled x 12 48 12 60 mph. d rt. Write a verbal model. Step 6: Interpret the results and write the answer in words.
miller_beginning_intermediate_algebra_4e_ch1_3
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