Final answer:
To determine when jet ski rental costs are equal between two companies, setup and solve a system of linear equations. The solution shows that the costs will be the same after rounding to the nearest whole hour, which is 6 hours.
Step-by-step explanation:
To find the number of hours for which the costs of renting a jet ski from two different companies are the same, we need to set up and solve a system of linear equations. Let x be the number of hours the jet ski is rented, and let y be the total cost to rent the jet ski.
The first company's cost can be represented by the equation y = 27 + 2x, where 27 represents the flat fee and 2 is the cost per hour. The second company's cost can be represented by the equation y = 16.50 + 3.75x, where 16.50 is the flat fee and 3.75 is the cost per hour.
To find when the costs are equal, we set the two equations equal to each other:
27 + 2x = 16.50 + 3.75x
Subtract 2x from both sides:
27 = 16.50 + 1.75x
Subtract 16.50 from both sides:
10.50 = 1.75x
Divide both sides by 1.75 to solve for x:
x = 6
So, after rounding to the nearest whole hour, the cost to rent a jet ski from both companies will be the same after 6 hours.