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Gilbert is training for a bike race. As part of his training, he does practice rides on portions of the actual race course. Gilbert's first practice ride covers 5 miles of the course, and his second practice ride covers 9 miles of the course. Between these practice rides, he increases his average speed by 2 miles/hour.

These functions model the time it took Gilbert to do each practice ride, where [tex]$x$[/tex] is his speed during the first practice ride.

\begin{tabular}{|c|c|}
\hline Practice Ride 1 & Practice Ride 2 \\
\hline[tex]$a(x)=\frac{5}{x}$[/tex] & [tex]$b(x)=\frac{9}{x+2}$[/tex] \\
\hline
\end{tabular}

The denominator of the function that models practice ride 2 represents the [tex]$\square$[/tex] .
To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, [tex]$\square$[/tex] the functions.



Answer :

GinnyAnswer
To solve this problem, let's carefully consider the context and details given.

1. The function [tex]\(a(x) = \frac{5}{x}\)[/tex] represents the time Gilbert takes for the first practice ride, where [tex]\(x\)[/tex] is his speed in miles per hour during the first ride.
2. For the second practice ride, he increases his speed by 2 miles per hour. Thus, if he rides at speed [tex]\(x\)[/tex] during the first practice ride, his speed during the second practice ride would be [tex]\(x + 2\)[/tex]. The function for the second ride is [tex]\(b(x) = \frac{9}{x+2}\)[/tex].

Given this context, let’s break down the two tasks:

1. The first blank refers to the denominator of the function for the second practice ride, [tex]\(b(x) = \frac{9}{x+2}\)[/tex]:
- The denominator [tex]\(x + 2\)[/tex] represents Gilbert’s speed during the second practice ride.

2. The second blank refers to combining the two functions to get the total time:
- To model the total amount of time Gilbert spent on the practice rides, we need to add the times for each ride.
- Therefore, we combine the functions [tex]\(a(x)\)[/tex] and [tex]\(b(x)\)[/tex] by adding them.

Now we can fill in the blanks:

The denominator of the function that models practice ride 2 represents the speed during the second practice ride.

To find a function that models the total amount of time Gilbert spent doing practice rides on the race course, add the functions.