Final answer:
The rental costs for company A and company B are the same at 100 miles driven. This is found by setting up an equation with the cost formulas from both companies and solving for the number of miles.
Step-by-step explanation:
To find the number of miles at which the rental costs for company A and company B are the same, we can set up an equation where the total cost of renting the truck from each company is equal. Let the variable m represent the number of miles driven.
Company A charges $90 per day plus $0.20 per mile, so their cost is represented as 90 + 0.20m. Company B charges $60 per day plus $0.50 per mile, represented as 60 + 0.50m.
Equating the two costs and solving for m:
90 + 0.20m = 60 + 0.50m
Moving the variables on one side and constants on the other:
0.30m = 30
Divide both sides by 0.30 to find m:
m = 30 / 0.30
m = 100 miles
The rental costs for company A and company B are the same at 100 miles.