A campground rents canoes for either $20 per day or $4 per hour. For what number or numbers of hours, h, is it more expensive to rent a canoe at the daily rate than at the hourly rate?

Rationale

It is more expensive to rent a canoe at the daily rate than at the hourly rate when h > 5.

When renting a canoe, the daily rate of $20 becomes more costly than the hourly rate of $4 when the number of hours exceeds 5. This is because renting for more than 5 hours results in a total hourly cost greater than $20 (i.e., $4 * h > $20).

A (h = 5) YOUR ANSWER

At h = 5, the cost of renting a canoe at the hourly rate is exactly $20 (4 * 5 = 20), which is equal to the daily rate. Therefore, this does not satisfy the condition of being more expensive at the daily rate.

B (h >= 25) YOUR ANSWER

While h = 25 does indicate that the daily rate is more expensive, the condition specifically asks for when it is more expensive, which starts at h > 5. Thus, this choice is unnecessarily restrictive as it only includes a subset of valid hours.

C (h > 5) CORRECT

This choice correctly identifies the condition where the hourly rental cost exceeds the daily rate, as for any hour count greater than 5, the hourly rate becomes more expensive than $20 (i.e., $4 * h > $20). This is the correct answer.

D (h < 5) YOUR ANSWER

For h < 5, the total hourly cost is less than $20 (4 * h < 20), making the hourly rate the more economical option. Therefore, this choice does not meet the requirement for the daily rate to be more expensive.

E (h ≤ 5) YOUR ANSWER

Similar to choice D, when h is less than or equal to 5, the cost of hourly rental is equal to or less than $20. Thus, this condition does not fulfill the requirement of the daily rental being more expensive.

Conclusion

The daily canoe rental rate of $20 becomes more expensive than the hourly rate when the rental time exceeds 5 hours. Therefore, the correct condition is h > 5, reaffirming that any rental time beyond this threshold results in a higher cost at the daily rate compared to the hourly rate.