Question 658940
37 mpg highway
30 mpg city.
drove 365 miles
consumed 11 gallons.
average mileage is 365/11 = 33.18181818 mpg overall average.
let x represent number of city gallons consumed.
let y represent number of highway gallons consumed.
you get the following equation:
x + y = 11
since he is getting 37 miles per gallon of x and 30 miles per gallon of y, then the total highway and city miles traveled would be found by the following equation:
37x + 30y = 365
you have 2 equations that need to be solved simultaneously.
they are:
x + y = 11
37x + 30y = 365
multiply both sides of the first equation by 30 to get:
30x + 30y = 330
subtract 30x + 30y = 330 from 37x + 30y = 365 to get:
7x = 35
solve for x to get x = 5
since x + y = 11, this means that y = 6
he consumed 5 gallons in highway driving and 6 gallons in city driving.
he drove 37 * 5 = 185 miles on the highway
he drove 30 * 6 = 180 miles in the city.
total miles is 185 + 180 = 365 which was the total miles he drove.
total gallons is 5 + 6 = 11
his average miles per gallon became 365/11 = 33.18181818 which is equivalent to 33 + 2/11 miles per gallon.