Question

The fuel cost per hour for running a train is proportional to the square of the speed it generates in km per hour. If the fuel costs ₹ 48 per hour at a speed of 16 km per hour and the fixed charges to run the train amount to ₹ 1200 per hour. Assume the speed of the train as v km/h.

If the train has travelled a distance of 500 km, then the total cost of running the train is given by the function:

Options

• `15/16 "v" + 600000/"v"`

• `375/4 "v" + 600000/"v"`

• `5/16 "v"^2 + 150000/"v"`

• `3/16 "v" + 6000/"v"`

Answer 1

`375/4 "v" + 600000/"v"`

Explanation:

Total cost of running train (let C) = `3/16 "v"^2"t" + 1200 "t"`

Distance covered = 500 km ⇒ time = `500/"v" "hrs"`

Total cost of running train 500 km = `3/16 "v"^2 (500/"v") + 1200 (500/"v")`

⇒ C = `375/4 "v" + 600000/"v"`