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The problem asks us to solve for the minimum and maximum number of hours for Andrew's road trip. He plans to drive 125 miles, plus or minus 20 miles, and maintain a speed of 50 miles per hour. 

### Step 1: Set up the equation
The equation for this situation can be expressed as an **absolute value inequality**:

\[
|d - 125| \leq 20
\]

This means that the distance \(d\) can vary by up to 20 miles from 125 miles, so the distance will be between 105 and 145 miles.

### Step 2: Solve for the time
The time it takes for Andrew to complete his road trip depends on the distance \(d\) and his speed. The time \(t\) is given by the formula:

\[
t = \frac{d}{50}
\]

We now calculate the minimum and maximum times by using the minimum and maximum possible distances (105 miles and 145 miles):

1. **Minimum time**:

\[
t_{\text{min}} = \frac{105}{50} = 2.1 \text{ hours}
\]

2. **Maximum time**:

\[
t_{\text{max}} = \frac{145}{50} = 2.9 \text{ hours}
\]

### Step 3: Conclusion
The minimum time for Andrew's trip is 2.1 hours, and the maximum time is 2.9 hours.

Would you like to see further details, ask any questions, or need help with the graph of the inequality?

Here are 5 related questions you can explore:
1. How would the time change if Andrew's speed were 60 mph instead of 50 mph?
2. How would you graph the solution for the distance range \(105 \leq d \leq 145\)?
3. What would the inequality look like if Andrew's distance varied by 30 miles instead of 20 miles?
4. How does changing the speed affect the solution of the inequality?
5. What is the relationship between speed, distance, and time in this context?

**Tip:** Always double-check your absolute value setup to ensure the inequality matches the range described in the problem.

On a road trip, Andrew plans to use his cruise control for 125 mi, plus or minus 20 mi. Write and solve an equation to find the minimum and maximum number of hours for Andrew's road trip.

Learn how to solve the absolute value inequality for Andrew's road trip. The problem involves solving for the minimum and maximum hours needed to cover a distance of 125 miles (plus or minus 20 miles) while traveling at 50 mph. This lesson covers algebraic concepts and the time-distance relationship, suitable for Grades 9-11.

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