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# The cost of fuel for running a bus is proportional to the square of the speed generated in km/ hr . It costs rs.48 per hour when the bus is moving at the speed of 20 km per hour. What is the most economical speed if the fixed charges are rs.108 for an hour,over and above the running charges

Arun
25763 Points
3 years ago
let F= fuel cost V= speed and K= constant
F=KV2
for the given condition, 48= K x 202
=) K= 3/25

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 (KV2 + A/V) A= rs 108/ hr
=) 2KV - A/V2 = 0
=) 2KV = A/V2
=) V3 = A/(2*(3/25)) = 108/(3/25)=900
=) V = 9.65 kmph
Ramesh saini
11 Points
3 years ago
let speed =v and cost c=kv² ,if cost is 48 then speed is20km/h then 48=k(20)² then k=3/25 now total cost=C=3/25×v² × x/v +108x/v (let distance be xkm) ,thenC=3vx/25 +108x/v now dC/dv=3x/25-108x/v² for max or min dC/dX=0 then we have v=30 now if v=30 then d²C/dx² is +ve so cost is minimum when v=30km/h