- #1
animboy
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Homework Statement
The fuel consumption of a river boat is kv3 litres per hour where k is a constant and v km/h is it's speed through the water throughout this question v > 4 km/h.
i) determine the fuel consumption for a trip of x km against a current of 4km/h and find the speed at which the fuel consumption is minimised.
ii) determine the most economical speed for a trip of x km against the current and return, assuming that the current is constant at 4km/h and that the same speed through the water is maintained in each direction.
Homework Equations
none in particular
The Attempt at a Solution
for part (i) is simply got
kv3 = k(4 + (x/t))3, where is x is the distance traveled against the current and t is the time taken to travel it. However every time I try to optimize it I get (x/t) = 0 , which means that the boat does not move a distance x at all! Is this an acceptable answer then? To say that fuel consumption is optimised when the boat does not move against the current at all?
I have not attempted the second part yet...
thanks