16. 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?
Answer: C
Renting a canoe at the daily rate becomes more expensive than at the hourly rate when h > 5.
When renting a canoe, the daily rate of $20 becomes more expensive than the hourly rate of $4 once the number of hours exceeds 5. This is because renting for 5 hours costs $20, which is equal to the daily rate, but any additional hour will increase the cost of the hourly rate beyond that amount.
A) h = 5
This option suggests that renting for exactly 5 hours would make the daily rate more expensive. However, at 5 hours, both the daily and hourly rates are equal, making this statement incorrect for the context of the question.
B) h >= 5
While this option includes the case where h equals 5, which is not more expensive, it incorrectly suggests that renting for 5 hours or more is valid. The daily rate is only more expensive when h exceeds 5, thus making this option incorrect.
C) h > 5
This is the correct option because renting a canoe for more than 5 hours will result in higher costs when using the hourly rate compared to the daily rate of $20. Specifically, at 6 hours, the cost would be $24 at the hourly rate, clearly exceeding the daily charge.
D) h
This option indicates that renting for 5 hours or fewer would make the daily rate more expensive than the hourly rate, which is incorrect. Up to 5 hours, the costs are equal, thus this option fails to satisfy the question's criteria.
E) h < 5
This option is incorrect as it implies that renting for fewer than 5 hours would make the daily rate more expensive. In fact, it is cheaper to rent hourly in this range, thus contradicting the question's requirement.
Conclusion
The correct answer, h > 5, accurately identifies the threshold where the cost of renting a canoe hourly exceeds that of the daily rate. All other options either misrepresent the relationship between the rates at 5 hours or incorrectly include scenarios where the daily rate is not more expensive. This logical analysis confirms that only option C provides the right condition for the cost comparison.