A steamship sails upriver from A to B against a current of three km/h. If the amount of fuel consumed per hour varies as the cube of the speed through the water, how fast should the captain order the ship to steam, if the fuel consumption for the journey from A to B is to be a minimum.

Answer 1

I gave this as a final exam problem in HS calculus many years ago.

Fuel=K1*(speedrelative to water)^3 *time

But time= distanceAtoB/(speedrelativewater-3)

fuel=K1*(speedrelativewater^3)distancAB/(speedrelativewater-3)
let s be speed relative to water
dfuel/ds= 3s^2*distance/(s-3) - s^3*distance(s-3)^-2

set to zero...

3s^2/(s-3)=s^3/s-3)^3

3=s/(s-3)
3s-9=s
2s=9
s=4.5

the minu

Answer 2

what does K1 stand for??

Answer 3

its the constant term; every time two things vary directly there's always a constant K that you have to consider.

Answer 4

Hi, Kavya! :D LOL