Question

engine coal consumption varies to (speed)²; When the engine speed is 50 km per hour then the cost per hour is 100 kg If the price of coal is 25 paisa per kilogram and the other cost of running the engine is 4 rupees per hour.What will be the minimum cost for the engine to go 300 km

Answer 1

Answer:

Let v be the velocity of the train in mile/hour, and q be the quantity of fuel used per hour in tons, then

q=kv

2

⟹2=k(16)

2

⟹q=

256

2

​

v

2

∴ Cost of fuel per hour =

2

1

​

×

256

2

​

v

2

=

256

v

2

​

∴ Cost of fuel per mile =

v

1

​

×v

2

256=

256

v

​

Cost per mile for other expenses =

20

11

4

1

​

​

×1v=

16v

9

​

∴ Total cost of journey per mile =

256v+ 16v9=( 16v − 4 V3) 2+ 323

​

Since least value of a square is 0, the least cost of the journey for 100 miles =

323×100= 32300=Pounds 9.7s.6d

Step-by-step explanation: