Final answer:
The rental cost for both Rapid Rental Car and Capital Cars is the same at 100 miles driven, with the cost equalling $80.
Step-by-step explanation:
To determine for how many miles the rental cost at both companies is the same, we can set up an equation where the total cost of rental, gas, and per mile driven for Rapid Rental Car is equal to the cost of rental, gas, and per mile for Capital Cars.
Let's let x represent the number of miles driven. The total cost for Rapid Rental Car is $40 (rental fee) plus $15 (for gas) plus $0.25 per mile driven, which is $0.25x. So the total cost for Rapid Rental Car would be 40 + 15 + 0.25x = 55 + 0.25x.
For Capital Cars, the total cost is $45 (rental and gas) plus $0.35 per mile driven, which is $0.35x. So the cost for Capital Cars would be 45 + 0.35x.
Now we set the two expressions equal to each other to find when the costs are equal:
55 + 0.25x = 45 + 0.35x
By subtracting 0.25x from both sides, we get:
55 = 45 + 0.10x
And by subtracting 45 from both sides, we have:
10 = 0.10x
To find x, we divide both sides by 0.10, resulting in:
x = 100
So, at 100 miles, the cost of renting a car is the same for both companies.
To determine what that cost is, we plug 100 back into one of the original equations:
55 + 0.25(100) = 55 + 25 = 80
Hence, the cost at which both companies charge the same rental fee is $80.