I assume "most economical" means lowest cost per mile.
The driver's wages:
$/mi = $/hr * hr/mi = $/hr / (mi/hr)
The truck:
$/mi = $/gal * gal/mi = ($/gal) / (mi/gal)
If speed is x, and y is cost/hr, including the driver's wages
y = 8/x + 1 * 1/(377/x)
y = 8/x + x/377
For minimum cost/mile,
y' = -8/x^2 + 1/377
x^2 = 3016
x = 54.9
A truck gets 377/x mpg when driven at a constant speed of x mph (between 25 and 75 mph). If the price of fuel is $1 per gallon and the driver is paid $8 per hour, at what speed between 25 and 75 mph is it most economical to drive? (Give your answer correct to the nearest full mph)
1 answer
1 answer