26. 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?
Answer: C
It is more expensive to rent a canoe at the daily rate than at the hourly rate when h > 5.
When renting a canoe at the daily rate exceeds the cost of renting it by the hour, this occurs for values of h greater than 5 hours.
A) h = 5
At h = 5, the cost of renting a canoe at the daily rate ($20) equals the cost at the hourly rate ($4 × 5 = $20). Therefore, it is not more expensive to rent at the daily rate; they are equal, making this option incorrect.
B) h >= 25
While renting for 25 hours would lead to a higher cost at the hourly rate ($4 × 25 = $100) compared to the daily rate ($20), this option overstates the requirement. The question asks for when the daily rate becomes more expensive, which occurs earlier; thus, this option is incorrect.
C) h > 5
When h exceeds 5 hours, the cost of renting by the hour becomes greater than the daily rate. For example, at h = 6, the cost is $24 (6 hours × $4), which is more than $20. This makes option C the correct choice, as it accurately identifies the condition where the daily rate is more expensive.
D) h < 5
For values of h less than 5, the hourly rate is less expensive than the daily rate. For instance, at h = 4, the cost is only $16 (4 × $4), which is cheaper than $20. Thus, this option is incorrect.
E) h ≤ 5
Similar to option D, h ≤ 5 includes values where the hourly rate is either equal to or less expensive than the daily rate. Since the question specifically asks for when the daily rate is more expensive, this option is incorrect.
Conclusion
The correct answer, h > 5, is definitive because it identifies the point at which the daily canoe rental rate surpasses the hourly rate. All other options either misrepresent the cost comparison or state conditions that do not satisfy the requirement of being more expensive.