Question

A motor vehicle has a maximum efficiency of 39 mpg at a cruising speed of 40 mph. The efficiency drops at a rate of 0.1 mpg/mph between 40 mph and 50 mph, and at a rate of 0.4 mpg/mph between 50 mph and 80 mph. What is the efficiency in miles per gallon if the car is cruising at 50 mph

Answer 1

38 mpg

Explanation:

Initial efficiency = 39 mpg

Initial speed = 40 mph

Final speed = 50 mph

The efficiency drop between 40 mph and 50 mph is given by:

`E_d = 0.1 (mpg)/(mph)*\Delta V`

The total efficiency drop from 40 to 50 mph is:

`E_d = 0.1 (mpg)/(mph)*(50-40)mph\\E_d = 1\ mpg`

Therefore, the efficiency at 50 mph is:

`E_(50) = E_(40) -E_d\\E_(50) = 39 -1\\E_(50) = 38\ mpg`