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 when h > 5.

When renting a canoe, the daily rate surpasses the hourly rate when the total hours exceed 5. This is calculated by comparing the daily cost of $20 to the hourly rate of $4 multiplied by the number of hours, h.

A (h = 5) YOUR ANSWER

When h equals 5, the cost of renting a canoe hourly would be $4 × 5 = $20, which is the same as the daily rate. Thus, this option does not represent a scenario where the daily rate is more expensive.

B (h >= 5) YOUR ANSWER

This choice includes h = 5, where the costs are equal, and does not account for values greater than 5. Therefore, it fails to capture the condition where the daily rate exceeds the hourly rate.

C (h > 5) CORRECT

When h is greater than 5, the cost of renting by the hour becomes higher than the daily rate. For example, at h = 6, the hourly cost would be $4 × 6 = $24, making it more expensive than the daily rate of $20. Thus, this option accurately describes when the daily rate is more costly.

D (h <= 5) YOUR ANSWER

This option includes scenarios where h is less than or equal to 5, where the daily rate does not exceed the hourly rate. Thus, it does not satisfy the condition where renting a canoe at the daily rate is more expensive.

E (h < 5) YOUR ANSWER

Similar to the previous choice, this option focuses solely on values less than 5, where the daily rate is always less than or equal to the hourly cost. Therefore, it cannot represent a situation where the daily rate exceeds the hourly rate.

Conclusion

To summarize, the daily canoe rental becomes more expensive than the hourly rate when the number of hours h exceeds 5. This situation is captured accurately by option C, which highlights the threshold where the costs diverge, reinforcing the importance of understanding cost comparisons in rental scenarios.