Certainly! To determine which inequality correctly represents the time [tex]\( r \)[/tex] it takes to drive the route under the given conditions, we can analyze the details provided.
1. Condition 1: If the bus driver leaves by 7:00 a.m., the route takes less than 37 minutes.
2. Condition 2: If the bus driver leaves after 7:00 a.m., the route takes no less than 42 minutes.
Let's interpret each condition individually:
- Condition 1: Leaving by 7:00 a.m. results in a route time of less than 37 minutes. Mathematically, we can express this as:
[tex]\[
r < 37
\][/tex]
- Condition 2: Leaving after 7:00 a.m. results in a route time that is no less than 42 minutes. This means the time [tex]\( r \)[/tex] is at least 42 minutes or more. Mathematically, we can express this as:
[tex]\[
r \geq 42
\][/tex]
Combining these two conditions, we find that the time [tex]\( r \)[/tex] can either be less than 37 minutes, or it must be equal to or greater than 42 minutes.
Thus, the correct inequality representing the time [tex]\( r \)[/tex] is:
[tex]\[
r < 37 \text{ or } r \geq 42
\][/tex]
So, the inequality that correctly represents the time it takes to drive the route is:
[tex]\[
\boxed{1: r < 37 \text{ or } r \geq 42}
\][/tex]
