the cost of fuel for running a train is proportional to square of speed generated in km/h.it cost rs 48/h when the train is moving at speed of 16km/h.what is its economical speed if the fixed charges are rs 300/hour over and above the running cost!

F=KV

^{2}

for the given condition, 48= K x 16

^{2}

=) K= 3/16

as fixed charge is in Rs/hr, it is proportional to 1/V. (time= distance/velocity)

for minima fuel cost, dF/dV = 0

=) d/dV (KV

^{2}+ A/V) A= rs 300/ hr

=) 2KV - A/V

^{2}= 0

=) 2KV = A/V

^{2}

=) V

^{3}= A/(2*(3/16)) = 300/(3/8)=800

=) V = 9.28 kmph

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