Question

A traveller employs a man to drive him from Sydney to Melbourne. Running costs of the car, which are also paid by the traveller, are k*v^3 dollars per hour, v is the speed and k is a constant. Find the uniform speed that will minimize the total cost of the journey.

Answer 1

time to go a distance d is d/v so the cost is (d/v)(kv^3) = dkv^2

Looks like k=0 makes cost=0.

I suspect a typo.