Question

The expenses per hour for plying steamer in a river is proportionate to cube of its speed. If the speed of the water current is x kin per hour, then prove that the maximum normal (prudent) speed of the steamer will be 2/3 km per hour if it flied against the current of the water.

Answer 1

Let velocity of steamer is u km/h and distance covered is S km.

According to question

Speed of water current = x km/h

and relative velocity of steamer = (u – x) k/h time take to cover the distance

T = s/(u - x) hour

Given expense per hour = Ku³ {K is constant}

Total expenses E = Ku³ . s/(u - x)