Let's analyze and break down the problem:

We have two car rental companies, A and B:

• Company A charges $45 per day to rent a car.
• Company B charges $30 per day plus $0.20 per mile driven.

The question asks: For how many miles driven is the cost at Company B more than the cost at Company A for a one-day rental?

Step 1: Set up the cost equations

Let $x$ be the number of miles driven.

• Company A charges $45 for a day regardless of miles, so its total cost is: $C_A = 45$

• Company B charges $30 per day plus $0.20 per mile, so its total cost is: $C_B = 30 + 0.20x$

Step 2: Write the inequality

We want to find when the cost of Company B is greater than the cost of Company A, so we set up the inequality: $30 + 0.20x > 45$

Step 3: Solve the inequality

Now, solve for $x$:

1. Subtract 30 from both sides: $0.20x > 15$

2. Divide both sides by 0.20: $x > \frac{15}{0.20}$

3. Simplify: $x > 75$

Conclusion

The cost at Company B will be greater than the cost at Company A when the number of miles driven exceeds 75 miles.

Would you like more details on how I solved this, or do you have any further questions?

Related Questions:

1. How would the inequality change if Company A charged by the mile?
2. What if Company B charged a higher per-mile rate, say $0.30 per mile?
3. How would the solution change if Company A's daily rate increased?
4. What if Company B had an additional flat fee?
5. How can you represent this comparison graphically?

Tip: Always check the units and make sure they match when comparing costs!