1. ## a nice question about the speed of a ship

Hi folks,

A ship is to make a voyage of 200 km at a constant speed. When the speed of the ship is v km/h the cost is $(v^2 + \dfrac{4000}{v})$ USD per hour.
Find the speed at which the ship should travel so that the cost of the voyage is a minimum.

So, v = 200/t where t is the time in hours.

Cost

$C =v^2 + \dfrac{4000}{v}$

$C = (\dfrac{200}{t})^2 + \dfrac{4000t}{200}$

$C = \dfrac{40000}{t^2} + 20t$

$\dfrac{dC}{dt} = \dfrac{-80000}{t^3} + 20 = 0$

$t^3 = 4000$

$t = 15.87$ hours

$V = 200/15.987 = 12.6$ km/h

this is the wrong answer. My book has 20km/h.

2. ## Re: a nice question about the speed of a ship

the total cost of the voyage is

$\displaystyle \left(v^2+\frac{4000}{v}\right)\frac{200}{v}$

3. ## Re: a nice question about the speed of a ship

I see! My method doesn't even make sense. The rate of change of cost, has nothing to do with minimising the cost of voyage.
Many thanks.