To understand what the rational term [tex]\(\frac{25}{r}\)[/tex] represents, let's break down the expression [tex]\(\frac{25}{r} + 3\)[/tex].
1. Distance and Speed Relationship:
- The term [tex]\(r\)[/tex] in the expression represents the average speed of the delivery truck.
- The term [tex]\(\frac{25}{r}\)[/tex] represents a time since it is the result of distance (25 miles) divided by speed (r miles per hour). When you divide distance by speed, you get time, specifically the time needed to cover that distance.
2. Interpretation of [tex]\(\frac{25}{r}\)[/tex]:
- Given that 25 miles is the distance the delivery truck travels, and [tex]\(r\)[/tex] is its average speed, [tex]\(\frac{25}{r}\)[/tex] is indeed the time required for the installer to travel 25 miles to reach the customer's home.
3. Overall Expression:
- The total expression [tex]\(\frac{25}{r} + 3\)[/tex] indicates the total time to complete the process—from traveling to the client's home to installing the door. The [tex]\(3\)[/tex] represents the constant time taken to install the door itself, which does not depend on the travel speed.
From these points, we can conclude that the rational term [tex]\(\frac{25}{r}\)[/tex] specifically represents the time it takes the installer to travel to the customer's home.
Therefore, the correct answer is:
C. The rational term represents the time it takes the installer to travel to the customer's home.
