64 Chapter 1 Linear Equations and Inequalities in One Variable Answer 7. Jody normally drives 60 mph. Solving a Distance, Rate, Time Application Example 7 A hiker can hike 1 mph faster downhill to Moose Lake than she can hike uphill back to the campsite. If it takes her 3 hr to hike to the lake and 4.5 hr to hike back, what is her speed hiking back to the campsite? Solution: The information given in the problem can be organized in a table. Campsite Moose Lake d (rate)(time) d x(4.5) d (rate)(time) d (x 1)(3) Distance (mi) Rate (mph) Time (hr) Trip to the lake x 1 3 Return trip x 4.5 Column 2: Let the rate of the return trip be represented by x. Then the trip to the lake is 1 mph faster and can be represented by x 1. Column 3: The times hiking to and from the lake are given in the problem. Column 1: To express the distance, we use the relationship d rt. That is, multiply the quantities in the second and third columns. Distance (mi) Rate (mph) Time (hr) 31x 12 Trip to the lake x 1 3 Return trip 4.5x x 4.5 To create a mathematical model, note that the distances to and from the lake are equal.Therefore, (Distance to lake) (return distance) Verbal model Mathematical equation Apply the distributive property. Subtract 3x from both sides. Divide by 1.5 to isolate the variable. Solve for x. 31x 12 4.5x 3x 3 4.5x 3x 3x 3 4.5x 3x 3 1.5x 3 1.5 1.5x 1.5 2 x The hiker’s speed on the return trip to the campsite is 2 mph. Skill Practice 7. During a bad rainstorm, Jody drove 15 mph slower on a trip to her mother’s house than she normally would when the weather is clear. If a trip to her mother’s house takes 3.75 hr in clear weather and 5 hr in a bad storm, what is her normal driving speed during clear weather?
miller_intermediate_algebra_4e_ch1_3
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