Final answer:
To determine where rental costs are equal for two truck companies with different pricing models, an equation was set up equating both costs, which are dependent on miles driven. The solution of this equation revealed that the rental costs are equal at 140 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 set up an equation where the cost of renting from Company A equals the cost of renting from Company B. Let m be the number of miles.
Company A's cost is $110 plus $0.40 per mile, which gives us 110 + 0.40m. Company B's cost is $40 plus $0.90 per mile, which results in 40 + 0.90m.
Setting the two costs equal to each other gives us:
110 + 0.40m = 40 + 0.90m
Subtracting 0.40m from both sides, we get:
110 = 40 + 0.50m
Now, subtract 40 from both sides:
70 = 0.50m
Dividing both sides by 0.50 gives us the final answer:
m = 140 miles
This is the number of miles for which the costs from Company A and B are the same. This conclusion is provided after comparing their daily rate and per-mile charge.