Section 2.7 Mixture Applications and Uniform Motion 177 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). 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 unknowns. 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 d rt. To set up an equation, recall that the total distance between the two families is given as 270 mi. Step 3: Write a verbal distance traveled by Family B ° ¢ total ° a b distancemodel. 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 x 48 a. Family A traveled 48 (mph). Family B traveled b. To compute the distance each family traveled, use Family A traveled: (48 mph)(2.5 hr) 120 mi Family B traveled: (60 mph)(2.5 hr) 150 mi d rt. x 12 48 12 60 1mph2. Distance traveled by Family A ¢ Step 6: Interpret the results and write the answer in words.
miller_introductory_algebra_3e_ch1_3
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