Final answer:
To find the number of miles, \(m\), it will take for Rent A Car and City Cars to cost the same amount, set the total cost equations equal to each other and solve for \(m\). The equation is \(16.25 + 0.90m = ? + 0.60m\) where "?" represents the rental fee and one-time fee for City Cars.
Step-by-step explanation:
To determine the point at which the costs are equal, set up an equation equating the total costs for both companies. For Rent A Car, the total cost is the sum of the rental fee, one-time fee, and the additional cost per mile. This is expressed as \(16.25 + 0.90m\). For City Cars, the total cost is represented by the rental fee plus one-time fee and the additional cost per mile, \(? + 0.60m\), where "?" is unknown. By setting these two expressions equal to each other, you create the equation \(16.25 + 0.90m = ? + 0.60m\).
To solve for \(m\), first, subtract \(0.60m\) from both sides of the equation to isolate the terms with \(m\). This results in \(16.25 + 0.30m = ?\). Then, subtract $16.25 from both sides to isolate \(0.30m\), yielding \(0.30m = ? - 16.25\). Finally, divide both sides by \(0.30\) to find \(m\), which gives the number of miles required for the costs of Rent A Car and City Cars to be equal. Solving this equation provides the specific mileage at which the total costs for both car rental companies are equivalent.