Introduction to Skating Costs: We Love Skating vs. Let’s Skate

Two popular skating venues, We Love Skating and Let’s Skate, offer different entry fees and skate rental charges. Understanding when the total cost of skating at each venue becomes the same can help you plan your visit more effectively. This article analyzes the cost structures and determines the number of hours required for the expenses to be equal.

Cost Structures at We Love Skating and Let’s Skate

We Love Skating charges an entry fee of $9 and $2.50 per hour for skate rental. The total cost at We Love Skating can be represented as:

C1 9 2.50h

Let’s Skate, on the other hand, charges $5.50 per hour for skate rental, and there is no entry fee. The total cost at Let’s Skate can be expressed as:

C2 5.50h

Setting the Costs Equal

To find the number of hours h for which the costs are the same, we need to equate the two cost expressions:

9 2.50h 5.50h

Rearrange the equation to isolate h:

9 5.50h - 2.50h

9 3.00h

Solve for h:

h 9/3.00 3 hours

Conclusion: You need to skate for 3 hours to make the costs at both venues equal.

Detailed Calculations

To verify this, let's calculate the total cost at each venue for 3 hours of skating:

Total Cost at We Love Skating:

Total cost 9 2.53

Total cost 9 7.50 $16.50

Total Cost at Let’s Skate:

Total cost 5.53

Total cost 16.50

Both calculations confirm that after 3 hours, the costs are indeed the same.

General Cost Analysis

Let's generalize the cost comparison for a more detailed understanding:

In the first case, the cost to get in is represented as c0 9. In the second case, there is no entry fee, so c0 0. The extra cost per hour is calculated as:

r 5.50 - 2.50 3.00 per hour

For the total costs to be equal, the accumulated extra cost over time must balance the entry fee:

rt c0

Solving for t:

t c0/r 9/3.00 3 hours

This confirms that 3 hours is the exact time when the costs are equal, regardless of the entry fee and rental rates.

Conclusion

The key takeaway is that 3 hours of skating is when the total costs of using We Love Skating and Let’s Skate become the same. Understanding this can help you in choosing the more economical option based on your skating preferences and the number of hours you plan to spend at the rink.