Problem 30

Given information

The graph shows the fuel consumption  of a car (measured in gallons per hour) as a function of the speed  of the car. At very low speeds the engine runs inefficiently, so initially decreases as the speed increases. But at high speeds the fuel consumption increases. You can see that  is minimized for this car when . However, for fuel efficiency, what must be minimized is not the consumption in gallons per hour but rather the fuel consumption in gallons per mile. Let’s call this consumption  .

Step-by-step explanation

According to the question, We can draw the diagram of a graph which is shows the fuel consumption of a car (in gallons per hour) as a function of the speed  of the car. At very low speeds the engine runs inefficiently, so initially decreases as the speed increases. But at high speeds the fuel consumption increases. You can see that  is minimized for this car when . However, for fuel efficiency, what must be minimized is not the consumption in gallons per hour but rather the fuel consumption in gallons per mile. Let’s call this consumption  .

Let quantity of fuel is gallons

And the time is hours   

And distance is  miles 

Thus,  

And   

So,