When driving to a friend's house, I can take either an expressway or a normal highway. The two paths have different lengths, and the average speed is higher on the expressway. The distance to my friend's house in miles vs. time in hours for the expressway path is graphed here. A. What total distance do I drive via the expressway? The equation d=-,t+35 models my distance, in miles, from my friend's house vs. time, in hours, if I travel by highway. What distance do I drive in this B. case? C. Which path gets me to my friend's house more quickly? How much time is saved?

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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#5: Which Way to Drive?

When driving to a friend's house, I can take either an expressway or a normal highway. The two paths have different lengths, and the average speed is higher on the expressway. The distance to my friend's house in miles vs. time in hours for the expressway path is graphed here.

**A.** What total distance do I drive via the expressway?

**B.** The equation \( d = -\frac{1}{2}t + 35 \) models my distance, in miles, from my friend's house vs. time, in hours, if I travel by highway. What distance do I drive in this case?

**C.** Which path gets me to my friend's house more quickly? How much time is saved?

### Graph Explanation

The graph illustrates the relationship between the distance to the friend's house and time when taking the expressway. It is a line starting at the point (0, 60) and ending at the point (6, 0). The x-axis represents time in hours, while the y-axis represents distance in miles. The slope of the line indicates a negative correlation, showing that as time increases, the distance to the destination decreases, reaching 0 miles in 6 hours.
Transcribed Image Text:#5: Which Way to Drive? When driving to a friend's house, I can take either an expressway or a normal highway. The two paths have different lengths, and the average speed is higher on the expressway. The distance to my friend's house in miles vs. time in hours for the expressway path is graphed here. **A.** What total distance do I drive via the expressway? **B.** The equation \( d = -\frac{1}{2}t + 35 \) models my distance, in miles, from my friend's house vs. time, in hours, if I travel by highway. What distance do I drive in this case? **C.** Which path gets me to my friend's house more quickly? How much time is saved? ### Graph Explanation The graph illustrates the relationship between the distance to the friend's house and time when taking the expressway. It is a line starting at the point (0, 60) and ending at the point (6, 0). The x-axis represents time in hours, while the y-axis represents distance in miles. The slope of the line indicates a negative correlation, showing that as time increases, the distance to the destination decreases, reaching 0 miles in 6 hours.
Expert Solution
Given

an expressway or a normal highwa. The two paths an expressway or a normal highway have different lengths, and the average speed is higher on the expressway.

The distance in miles vs. time in hours for the expressway path is given by graph.

To find 

A. Total distance via the expressway.

B. The equation d=-t/2 +35 models distance, in miles vs. time, in hours, if I travel by highway.

To find distance in this case?

C. To determine which  path is quicker. And how much time is saved?

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