Let's break down the solution into detailed steps for clarity:
1. Understanding the Functions:
- For Practice Ride 1, he covers [tex]\(5\)[/tex] miles at a speed of [tex]\(x\)[/tex] miles per hour:
[tex]\[
a(x) = \frac{5}{x}
\][/tex]
This function gives the time in hours for the first practice ride.
- For Practice Ride 2, he covers [tex]\(9\)[/tex] miles at a speed of [tex]\(x + 2\)[/tex] miles per hour:
[tex]\[
b(x) = \frac{9}{x + 2}
\][/tex]
This function gives the time in hours for the second practice ride.
2. Denominator of Practice Ride 2:
- The denominator of the function [tex]\(b(x) = \frac{9}{x + 2}\)[/tex] is [tex]\(x + 2\)[/tex], which represents Gilbert's speed during the second practice ride.
3. Total Time Function:
- To find the total time Gilbert spends on both practice rides, we need to add the time functions for Practice Ride 1 and Practice Ride 2.
- Therefore, the function that models the total amount of time Gilbert spent doing practice rides on the race course is:
[tex]\[
\text{total\_time}(x) = a(x) + b(x) = \frac{5}{x} + \frac{9}{x + 2}
\][/tex]
Select the correct answer from each drop-down menu:
1. The denominator of the function that models practice ride 2 represents the speed during the second practice ride.
2. To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, add the functions.
