(TRANSPORTATION COST) A truck is hired to transport goods from a factory to a warehouse. The driver’s wages are figured by the hour and so are inversely proportional to the speed at which the truck is driven. The cost of gasoline is directly proportional to the speed. Express the total cost of operating the truck as a function of the speed at which it is driven.
To express the total cost of operating the truck as a function of the speed at which it is driven, we need to consider the driver's wages and the cost of gasoline.
Let's assume that the driver's wages per hour are represented by the variable D, and the cost of gasoline per hour is represented by the variable G. Additionally, we'll denote the speed at which the truck is driven by the variable S.
Given that the driver's wages are inversely proportional to the speed, we can express the driver's wages as a fraction of a constant K and the speed S:
D = K / S
Similarly, the cost of gasoline is directly proportional to the speed, so we can express it as the product of another constant C and the speed S:
G = C * S
Now, the total cost of operating the truck is the sum of the driver's wages and the cost of gasoline:
Total Cost = D + G
Replacing D and G with their equivalent expressions, we have:
Total Cost = (K / S) + (C * S)
Simplifying, we can rewrite this expression as:
Total Cost = K / S + C * S
Thus, we have expressed the total cost of operating the truck as a function of the speed at which it is driven.
wages = k/v
gas = c v
total = k/v + c v