Final answer:
To find out which bike rental is more favorable, compare the total costs of Mike's Bikes and Rick's Rides based on hours rented. Without the specific rental duration, a definitive answer cannot be given, but the hourly rate is cheaper at Mike's Bikes, and the initial fee is lower at Rick's Rides.
Step-by-step explanation:
The student has asked which bike rental option is more favorable for a day at the beach. To determine the more favorable pricing between Mike's Bikes and Rick's Rides, we need to compare the total costs for renting a bike for a certain number of hours at each service. Let x represent the number of hours Alex rents the bike.
For Mike's Bikes, the total cost (T) can be represented by the equation T = 6x + 18, where 6 is the hourly rate and 18 is the one-time rental fee.
For Rick's Rides, the equation for the total cost is T = 9x + 6, with 9 as the hourly rate and 6 as the rental fee.
The break-even point, where the costs from both services are equal, occurs when 6x + 18 = 9x + 6. Solving for x gives the number of hours at which point the pricing is equal. If Alex plans to rent a bike for fewer hours than the break-even point, Mike's Bikes would be more favorable; for more hours, Rick's Rides would be. Without knowing the exact number of hours Alex plans to rent the bike, it's not possible to definitively say which option is more favorable. However, the cost per additional hour is cheaper with Mike's Bikes, and the initial rental fee is lower with Rick's Rides.