Hello, chibiusagi!

We're having trouble reading what you wrote.

Let me take aguessat what you meant . . .

A traveller employs a driver from Sydney to Wollongong at dollars per hour.

Operating cost of the car is dollars per hour,

where km/hr is the speed and is a constant.

Find the uniform speed that will minimize the total cost.

Let = number of hours of driving.

The driver is paid dollars per hour for hours.

. . This will cost: . dollars.

The car will cost dollars per hour for hours.

. . This will cost: . dollars.

The total cost is: . dollars. .[1]

Let = distance from Sydney to Wollongong (km).

. . At km/hr, it will take: . hours. .[2]

Substitute [2] into [1]: .

Minimize: .

Multiply by

Therefore: .