Final answer:
After setting up and solving the equation 240 + 0.25m = 180 + 0.40m, we find that the cost of renting a car and a truck is the same after traveling 400 miles.
Step-by-step explanation:
To find after how many miles the cost of both a rental car and a rental truck will be the same, we need to set up an equation where both costs are equal. Let's denote the number of miles as m. For the car, the cost will be $240 plus $0.25 per mile, which gives us the cost equation 240 + 0.25m. For the truck, the cost will be $180 plus $0.40 per mile, resulting in the cost equation 180 + 0.40m.
We equate the two expressions to find the value of m that makes them equal:
240 + 0.25m = 180 + 0.40m
To solve for m, we first move the variable terms to one side and the constant terms to the other:
0.25m - 0.40m = 180 - 240
-0.15m = -60
Next, we divide both sides by -0.15 to isolate m:
m = -60 / -0.15
m = 400
Therefore, after 400 miles, the cost of renting both vehicles is the same.